Another reason could be tires: maybe you want to run more robust tires or tires with a bit of tread when you are out for a training ride — asking someone for a ride home sucks. Almost as much as walking home. (Ask me how I know.)
Maybe, but I wouldn’t think of wheelsets in terms of race wheels vs. training wheels. But rather wheelsets with different purposes. Differentiating properties could be wheel depth, cassettes or on-road vs. off-road tires. The other thing is, the more specialized you get, the less good they become under normal circumstances.
I’d probably keep things simple and start out with a single set of nice wheels that are quite versatile, i. e. about 45 mm deep and relatively wide. If you really identify a need for a second pair of wheels, then you could still grab a second pair. And if I needed a spare wheelset for emergencies, I’d probably go for a cheap aluminum wheelset that I’d never use (hopefully).