Definitely late to the party on this one, but here's my two cents. Frenzy is supposed to be a wild abandon focus on damage and carnage over self preservation. A simple and effective fix for this is to double the damage bonus afforded by Rage, but the barbarian loses any and all damage resistances they have for the duration. While still being a mound of hit points, it's not a huge threat, but it is certainly enough of a downside to make one think twice about losing any resistances when fighting say an ancient dragon. This solution also allows for two weapon barbarians to get the effectiveness out of the ability. Combine it with Reckless Attack and you get a fairly large amount of risk/reward going.

Since I apparently never posted this in this thread (🙄), here is how I fixed the Berserker:

3rd-level Path of the Berserker (FIFY) feature

You can go into a frenzy when you rage as part of the same bonus action, or while you are raging (no action required). While in a frenzy, you ignore the effects of Exhaustion, and can spend a bonus action on each of your turns to make a single melee weapon attack. When your rage ends, so does your frenzy.

Whenever you use this feature more than once between long rests, at the end of each use after the first you gain one level of Exhaustion.

Could give Them the stunned effect for a 1 minute or something

Stab wound take MUCH longer though.