given nobody makes such fast zooms, it must be difficult to get decent image quality out of them, even with a smaller (APS-C) sensor
Kinda - if you go to the slightly smaller sensor FourThirds world, they have two f/2 zooms: 14-35mm
. Sit down before you look at the price though.
I've also seen some long f/1.4 or was it f/1.8 zooms in C-mount (think it was a Sony 18-100mm) which was tempting me but someone else beat me to it. They cover an even smaller image circle than 4/3 though.
I think f/2 zooms in APS-C are very possible, but they would be of even shorter range than existing f/2.8 zooms and the price would be rather insane. So overall you might as well stick to the f/2.8 zooms or get the faster primes.
As for the long term survival of APS-C DSLRs, that depends entirely on what happens with mirrorless systems. Can they gain enough traction to displace APS-C DSLRs, leaving only full frame DSLRs taking a niche at the high end. Or will mirrorless fail to make an impact, where APS-C DSLRs will remain a sweet spot for a long time? We'll have to wait and see.