I was thinking of saying the same thing but resisted because I realized that 'voice coils' can 'cheat' a bit. There could be track marks on the platter so the heads could watch for a data pattern and make the voice coil seek in and adjust heuristically to the correct position. On the other hand, old VOMs (Volt/Ohm meters) tended to have a coil to direct the indicator needle and they seemed reasonably accurate.
Yes, exactly; feedback can make almost anything accurate. That's why most analog electronics are built using op-amps.
The old VTVMs were pretty accurate, but the meter mechanism was fairly expensive and pretty delicate. It also needed a fine adjustment for zeroing the dial, which needed to be tweaked every time you used it.
Stepper motors also have the advantage of being "digital", in that they move in discrete steps. They avoid having any analog circuitry.