i think heros are exceptional people of exceptional ability so my home brew is any and all permanent rolls can never result in 1s so any level up or base stats are rolled with 1s always rerolled.

when drawing up a new character i now pool the dice. there are 6 stats and i allow 4 dice per stat that is 24 6 sided dice you roll all 24 dice until there are no more 1s in the pool then you remove the 6 lowest dice.  then from the pool you can combine any 3 dice to create each of 6 stats likely granting you a near 100% chance at least one 18. but after combining one 18 stat i dont allow any more 18s unless you have like fourteen 6s then you have no choice but to make more than one 18

then upon each level up what good is an unlucky barbarian that keeps rolling 2s for hit points on each level up hahahaha, thats no hero!!!! so upon level up all my players and monsters/NPCs get the ability to reroll 1s all day but heres where it gets juicy. what ever your constitution bonus is, is one reroll of up to your con bonus so if your con bonus is +4 then you can reroll any 2-4 once and heres the kicker that maybe im to kind all level up hit point rolls are made with advantage.... roll a second die and pick the roll you prefer.

maybe i should use advantage or the con bonus reroll but not both i just cant in good conscience allow my players to roll lower than their bonus or maybe i can cheese it and say any rolls equal or less than your con bonus can be rerolled until you get a roll greater than your con bonus. maybe this is the most simple!!!!

I'm not sure what the question is ... as a DM you can decide how the characters will be created and how they will level up. If you want a game with really high stats and hit points then go for it, it is the game that you and your players apparently want to play and that is perfectly ok.

As DM, you will be adjusting encounters for the party capabilities anyway so it honestly really makes little or no difference. If the higher numbers make your players feel more powerful and you want their numbers to really stand out compared to a standard 4 hit point commoner with 10 in each stat then, again, go for it - whatever makes the game fun for you and your players.

If you enjoy this method just use it. Seems a bit complicated to me. And rolling 24 d6’s won’t guarantee high numbers even with rerolling 1’s. A bit higher maybe but not tremendously so. But I’m no statistician, lol. 

For HP, if I wanted higher numbers maybe allow the roll two die keep the highest and nothing below the flat HP average provided. So minimum 4 for d6 hit die up to 7 for that barbarian’s d12 plus con. 

I’ve seen some that roll multiple sets of stats 4d6 discard lowest and pick the best set or even mix and match. Or use point buy and up the number of points. 

If this is fun, then great! The question is, do your players understand the rules, or can you talk them through them, so this all works out.

For myself, I'm afraid of dice, so I like the point buy and I take the average for my levelup hit points. 

(I also appreciate that point buy means that all the characters at the table start with relatively similar resources, ie that you don't have one player with extremely high stats and another with substantially lower stats trying to play together in a long term campaign.)

You need to decide what works best for you and your table.  As long as everyone is having fun, it's all good.  It's not a bad idea to get input though.  It is easy to overlook something that could become a potential problem down the line.

I can tell you what my group does.  But remember, just because it works for us, doesn't mean it will work for everyone.

For stats, when starting a new campaign / one shot, etc.  All the players roll a group of six stats using 4d6, dropping the lowest.  The group then decides which set everyone will use (each player decides what rolled stat goes to which ability).  This way everyone has the same starting base.

For HP, when rolling for HP we take the dice roll or the average, whichever is higher.