Berserker Redux

I like where you are going with this version of the Berserker, but I can't get past the 10th level ability. I honestly feel like we could work on the feature that is already there. Maybe instead of having the Intimidating Presence take an entire action, it could be a bonus action. That way it's like you are making a choice between more damage or the crowd control, also I would have the DC based off the STR score rather than CHA.

Hey thanks mojiquee for your response, late or not.

I am aware of the Reckless Attack feature, yet I don't know if it's something that you should always use. Sure typically a raging Barbarian will only take half damage but he is getting hit that more often. And not getting hit equals 0 damage.
So tactically speaking I would not be in favor of Reckless Attacking all the time, if you can be targeted by multiple enemies.

Looking at the numbers at lvl 6
Yet as you do reckless attack every single turn, than yes, you have 29,25% chance on rolling a critical hit. Yet, the chances of that critical hit killing a creature, that's difficult to estimate, so I would estimate it somewhere between 1/4 and 1/2, let's assume 1/3. So would hypothetically give about 10% chance of healing a level of fatigue a turn when you can make 3 attacks a turn. Which seems reasonable with one level of fatigue. yet with two levels of fatigue this becomes a lot more tricky as you lack the speed to ensure that you are in melee range each turn.

Let's now look at the average length of a combat, let's assume that would be 7 Turns, if we assume that you have 6 turns with 3 reckless attacks, you'll have 60% change of healing 1 level of exhaustion. So those are indeed very good odds.
It would just be a real bummer if you manage to drop out of rage early and/or just don't get to kill anyone with a critical. Because now you are at level 2 exhaustion and I don't see that working well with a Barbarian. Now the opponents can ignore him more easily and he will need to make Ranged Attacks to stay enraged.

So I think this subclass will work if it get's those heals in, if you don't, then it feels really restrictive as you don't have much to fall back to. Of course there can be divine caster in the party who has greater restoration just to fix you if you didn't make it.

Yet I would like to propose a different healing mechanism, which is more reliable to trigger. I was thinking along the lines of "spilling your opponents blood in a splatty manner." So at first I thought: if you kill a creature by inflicting at least 15 damage with the killing blow. With +3 dmg from STR and +2 from Rage, this will be about 1/6 times you kill a creature. This will increase of course when damage increases. Quite dramatically if you combine this with Heavy Weapon Master. But maybe that isn't a bad thing.

You could go another route: when you roll maximum weapon damage on the killing blow, you regain an exhaustion level.  This would encourage d8 (12,5%) - d10 (10%) or d12 (8,33%) weapons as they will roll maximum damage a lot more easily than 2d6 (2,8%) weapons.
I you take heavy weapon fighting style, these changes go up by: d8 15,6%, d10 12% and d12 9,7% for 2d6 this changes little as both dice need to roll 1-2 and 6's afterwards.

But maybe I'm overthinking the exhaustion regeneration and it's fine to be exhausted and your barbarian needs to relax for a while before becoming fully operational. One part I miss in the first read is that you mechanic for Exhaustion regeneration can also happen in a regular rage, you don't need to Frenzy to regenerate.

I was re-reading you introduction text of the subclass and noted this:
Between a means of healing exhaustion and having up to four attacks a round at level 10 (two standard Attack action attacks, one additional Attack action attack while in a Frenzy, and Frenzy's bonus action Attack), I think this makes going into Frenzy very inviting and worth it knowing that you can shake it off, and making Berserker worth choosing in the face of Totem Barbarian.)
As I read the Chaotic Frenzy ability, it would lead me to think that you are making 7 attacks per turn. 3 Per Attack  Action and one extra through Bonus Action, while in Frenzy. Might this be a little bit over-powered?
At lvl 10 with both ASI in STR, and a Great-axe that would be d12 + 8 damage, let's assume Reckless Attacks, (because, hello 7 attacks!) and that 70% of the attacks hit. That on average 71 damage per round, spread over 7 targets in melee.

With this in mind the Subclass becomes an absolute power house while in Frenzy. The problem might even be that he is too effective and obliterates anything that come nearby and that he runs our of targets, but that's what you want, right?
Yet outside of Frenzy, there isn't much offered by this subclass until level 14.
So that's why I would like to see a level 10 ability that doesn't double down on Frenzy, it might boost it to 2 extra attacks per bonus Frenzy action and give something else, like a fear, based on CON DC, once per day or the likes.

Okay, this response is super late, but you should really consider looking at the class' base features before judging it based on what you can do with multiclassing. Reckless Attacks give you advantage on attacks at will, at an imposed advantage at getting struck. So, with this berserker, you're taking massive damage and getting hit a lot, but let me be clear. You are not rolling just four attacks per round, you're rolling 8 d20s and taking the  most impressive rolls. With advantage, your chance to crit (nearly) doubles, effectively becoming a Champion in that regard, so much so that I'd be worried about letting someone actually multiclass into Champion and get a combined total of 19% crit rate. That's right out, but then again, so is reducing the damage from the average 148 damage of every single attack a Terrasque can dish out on its turn down to a whopping 65 damage with the bare minimum of a Barbrogue. The level 8 Barbrogue, with Uncanny Dodge and Rage, can survive going toe to toe with a Terrasque for more than six seconds without any help. With one more level in Barbarian and some optimization at chargen (Vuman with Tough), he can survive that assault a second time. Assuming no crits, of course. Regardless, that is busted. Lastly, a Barbarian doesn't have to be in a frenzy to get their exhaustion relief, so there are safer ways to play against exhaustion than to gamble at it.

Anyhow, the chances of getting a crit with advantage are 9.75%. That's nearly as effective as an Improved Critical, but it gets better. With Berserker's default ability of bonus action attacks during Frenzies, that's a second attack at level 3. Between two attacks, the chances of either of those being a critical is 19.50%. That's around 20% chance per turn to cure the exhaustion you've brought on yourself with that rage the moment you take it. You're dishing out damage like crazy at this point. Two greataxe swings with +3 Strength, and +2 Rage, let's assume our Barbarian is, averages at 11.5 damage an attack and 23 damage a round. That's a lotta damage. On top of that, there's a 10% chance to crit to deal the maximum of 17 damage instead of 11.5, or double depending on the rules. Best case scenario, that's 34 damage. At level 3. The Barbarian doing this damage has about 38 HP. Not only is this guy in the realm of one-turn killing anyone else in the party, there's many CR3 monsters that he could kill in two turns.

At Level 5, things get real serious, as he can now recklessly attack three times. Those odds are around 29.25% that any of those will be a 20, per turn. At level 5, a Fighter is expected to do around maybe 18 damage, which isn't that bad given it's consistent damage that doesn't fail and he's got respectable AC and health to boot. The Barbarian, with his 29% Critrate? With the ASIs in Strength, his trusty greataxe, and three frenzious attacks, he can deal around 37.5 damage without critting. This isn't anything to scoff at. Even without Frenzy, it's still really good; 25 damage, but more importantly, a 20% chance to restore exhaustion per turn without having to go into a frenzy for it. That's really good for something you do naturally while doing what you do best; killing things.

Also, I've the suspicion that you've never had to deal with exhaustion outside of being a berserker. Well, here's a trick: as a berserker, exhaustion doesn't scare you, because you can heal it back, so take every opportunity to take it. Stay up all night on a lone watch, run a marathon, down a liter of whisky in one action, fight anyone, anywhere, anytime, Constitution saves be damned if you make it or break it, doesn't matter. You're a berserker, and the blood of your enemies are all you need to persist.

I would suggest to include the ability to heal exhaustion from 3rd level.
The reasons are twofold: most other primal paths offer a benefit which is always active during rage from 3rd level. Without the ability to heal exhaustion, you probably will shy away from using the second Frenzy.
Secondly, it's only on a Crit that the healing occurs, which is at base 5% of the time. Which means once in 20 attacks. With improved Crit it bumps up to 1 in 10, which might be an OP build if you reach lvl 10 and Chaotic Frenzy.
But still you only heal exhaustion when you have gained it, so it's still situational.

So let's look at the actual numbers: up to Lvl 4 you can make a maximum of 19 attack during a rage of 1 minute. Almost 0.95 crit and 1.8 crit improved Crit
Lvl 5 -9: max attacks in 1 minute: 29 attacks, 1.45 Crit and 2.9 Crit with improved Crit
Lvl 10+: max attacks in 1 minute: 38 attacks, 1.9 Crit and 3.8 Improved Crit

If we assume that you can take 7 Rage turns (out of max 10) as an average. These numbers become:
Lvl 3-4: 0.65 Crit and 1.3 imp Crit
Lvl 5-9: 1.00 Crit and 2.00 imp Crit
Lvl 10+: 1.30 Crit and 2.60 imp Crit

So this makes me conclude that you should change Chaotic Frenzy, even without improved crit build from 3 lvl of Fighter the downside of exhaustion is reduced to only 1 lvl, because the next time you go into a Frenzy you are almost certainly going to heal that level of exhaustion, so you will almost never have more than one level of exhaustion to work with. 
Yet I can see that constantly rolling on disadvantage at all your ability checks kind of restricts your effectiveness almost solely to combat, so it's still a disadvantage.

I would suggest to find a different feature than Chaotic Frenzy, as it is basically improved Frenzy, only you gain 3 attacks on a basic attack action, instead of 1 extra attack on the Frenzy Bonus Action. So I miscalculated as the first turn you enter the Frenzy you already gain the bonus attack from Chaotic Frenzy.

I do like Intimidating Pressence as it gives you an option beyond mindless rage and destruction and it's very thematic. I would change the Charisma modifier to Strength, as it is more fitting, your opponents are frightened by your physique, not by you eloquent speech. Although a beastly howl can never hurt but you have to back it up by bulging biceps and a huge weapon. So I could see a little bonus of +1 for a Heavy and Two-Handed weapon to the DC. I would also reset the feature after a short or long rest instead of the 24 hours after a creature successfully saved seems a little off. I do like the fact that you can't use this feat when an opponent broke the fear, because this will hurt your ego as a killing maniac.