I've been suggesting the opposite would happen so I'm extremely confused by this.
The problem the Frenzy creates is that, if they use it too early in the adventuring day, you're basically weakening the entire party for the rest of the day outside of combat (get it to 3 and its inside of combat, too).
By 3rd level, I trust my players that understand the game enough to realize kobold and friends aren't worth taking a level of exhaustion. Nor is the first fight in the game.
You can't tell me that a 5th level wizard should blow their fireball on the two goblins across the hall. I mean, look, I know, what if they do? What if they dump all their spellslots in the first two encounters in the adventure? Now they're worse than the martials and contribute basically nothing because cantrips are only so useful OoC.
They're not going to do that, because players aren't really all that braindead. 1st level exhaustion can be bad but...what? Were you in "the dungeon of stuck and/or breakable doors and other physically strong obstacles?" It's not like you're using a strength check every single OoC opportunity. Again, if it's
that important, they can expend a rage for it.
It's so easy to forsee the adventure. It's not a mystery when it's close to ending. You have only a couple rooms left, the guy your facing literally was the villain the entire time, the NPC revealed themselves to be the traitor all along. You can't really miss a climax unless you've never seen any type of fiction.
Which sounds like the climax of a 3rd level adventure? The kobolds ambushing you while walking into the green wyrmling's lair, or the green wyrmling with 2 kobold sidekicks?
Just don't be braindead and a frenzy Barb is perfectly fine.