Berserkers are probably the worst designed 5e subclass, probably even worse than champions. Having a subclass feature that actively kills you for using it is horribly punishing, hence why every other Barb subclass is way more popular in TT.
There's a lot of homebrew solutions to this but the one I personally use in my TT sessions is to take a page from how Rage worked in 3.5e/Pathfinder 1e. Instead of giving you a full level of exhaustion when your Frenzy ends, you should only get a "temporary" level of exhaustion that lasts for a minute and cannot kill you. If you want it to be more punishing, you can make it so that if you Frenzy again within that minute it becomes a permanent level of exhaustion. This way you're still punished for letting your rage drop mid-battle, but you're not actively killing yourself by using your subclass feature. You'll atleast be able to Frenzy multiple times per day without having to spend multiple days resting in order to not die.
