I'd always heard the problem with class AB was less that both devices were on, but that when it's switching off one side near the zero point, that action added noise.
There were a lot of branded tricks in the dying moments of "stereo as a status symbol" (early 1980s) which tried to mitigate this. (Technics New Class A, JVC Super-A, etc.)
think of it this way: if you apply a sinusoid into a power storage, when the device (or the top/bottom device on its own) conducts 100% of the time, it is class A. When it conducts <50% of the time, it is class C. When it conducts >50% of the time (i.e. near the middle, both devices conduct), it is class AB. When it exactly conducts 50% of the time, it is class B.
Turns out at the crossover point, when it's is class AB, you get something called gm doubling where the large signal gain goes up because both devices are conducting and therefore providing gain. When you're in class C (incorrectly called class B by noobs), no device conduct near the middle so you get crossover distortion in the opposite direction. In class B, you theoretically get near-perfect handoff which makes the crossover distortion minimal (at least compared to class A)
There were a lot of branded tricks in the dying moments of "stereo as a status symbol" (early 1980s) which tried to mitigate this. (Technics New Class A, JVC Super-A, etc.)