But not with literally just 1 level of exhaustion.
Regarding ChrisCarlson's post:
Wow, congrats, you saw a 1 in 400 chance occurrence. If you're saying that disadvantage has such a small impact, then knock your socks off. For the rest of us that passed basic mathematics, we'll prefer to take our 1/2 damage from nearly all sources over a cumulative -5 to Initiative, Grapple chances, Perception (PP goes down by -5), etc. to get a bonus action attack that a feat you'll probably be picking up anyways (Polearm Master and/or GWM) would provide you with either guaranteed or semi-regularity.
But hey, if you go to LA Strategiecons, chances are pretty decent we can end up at the same table. You bring your disadvantaged Barbarian and I'll bring my not-disadvantaged one. Let's see how it plays out.