Motor windings can and do fail, but not on any regular basis. Some of the causes would be thermal cycling which can create friction in the windings and wear insulation, or foreign objects getting into the motor and damaging the insulation, or plain ol' insulation degradation due to dust, dirt, and elements.
A real motor shop will have the capability to perform hi-pot testing on the windings, and would be able to tell pretty quickly if the insulation had been compromised. If so, rebuilding the motor wouldn't be justified unless it is cost-effective to rewind it, and for most small motors (pool pumps included), that's not the case.
If, however, a motor shop rebuilds the motor, it should get bearings, cap, any worn components as mention above, and also get insulation testing and vibration testing, which should identify bent shafts or unbalanced rotors. You should get a motor capable of a nice long productive life. Again, if the windings are compromised, the same is not true.
I will say, though, that the motor shop where I used to work, so many years ago, did stock Hayward pumps, though, 'cause so many pool pump motors simply weren't up to a rebuild.