Peter, true, I haven't seen it in here to speak of---but I am still a newbie by most of you folks' standards. I've seen a few occurences in Audio Amateur and its later incarnations (in fact I bitched about one where I thought the guy didn't understand how current sources/sinks worked).
For driving really low Z loads it does have the disadvantage of taking away from the maximum available current in one polarity. But who really drives loads that low very often? We all sleep better knowing we can perhaps, then drive a little cable C with maybe 10k at the other end, mostly.
It also is just shifting the region of crossover distortion to a different output voltage, unless output loading is really light---only so much you can do if the IC has crossover distortion to begin with. Intuitively that should be where the signal is such as to make that distortion less audible. But I think Self argues somewhere that rich class AB isn't a good idea---that if you're going to do class A, go pretty much whole hog.
(An approach that avoids some of the disadvantages of class AB, without the dissipation of class A, keeps a bit of quiescent current flowing in both sections of the output stage, regardless of output current, to keep the transistors' Ft's from going to zero. But it is tricky, and usually involves diodes somewhere with their own turnon/off behavior).
I say if it is really loud when you get to turning one half of the output off, who hears it anyway---but then I'm usually reaching for earplugs at that point anyway, or running from the room.