Exhaustion as a Balancing Factor in Powerful Low-level Spells

[Man_Over_Game]

Those aren't punishing the character for using it, except maybe the heavy armor without the strength. They aren't worse off than they were. For a published example of someone being punished for doing what they are supposed to be doing see Berserker Barbarian. Being published doesn't make it a good idea.

Reckless Attack causes all incoming attacks to have Advantage until your next turn.

Rage prevents you from casting spells, which has gotten in the way of many Barbarian/Warlock hybrids. That may not be applicable to you, but that doesn't mean it isn't ever applicable.

Additionally, Berserker Barbarian doesn't state that you have to Frenzy. It adds it as an optional cost when you Rage. You can still Rage normally. The reason Berserker is bad isn't because of Frenzy. It's because you have to choose between Frenzy and a different subclass feature. If something worthwhile was added to the Berserker (say, regenerating 1/2 of your Barbarian level in HP each turn while Raging), then it wouldn't be a bad choice.

But instead, we have to choose between Exhausting ourselves for 1 attack each turn by spending a BA, or getting additional Radiant damage per turn at no additional cost.