Lethargy if a Frenzied Rage drops does sound like a good possible drawback.
Other than that, the only thing I can think of to substitute for exhaustion would be like a -2 or -3 to AC while in a Frenzied Rage, because their defenses are even less when they're in the mindless fury of a frenzy. That at least is easier to do in a computer game than in pen and paper because the computer can do it instead of the player needing to remember.
