The tire is the black rubber that's mounted to the wheel. Tire shops don't give you a new wheel when you get a flat tire.

The "edge cases" make a simple task like this more difficult. What if the nuts are stripped? What if the terrain under/around the car is uneven or not solid ground? What if it's raining or snowing or hailing? What if the driver of the car is irrationally upset and kicks your tire-changing robot over? What if a tire change was requested, but it's clear (to a human) that there is more work that needs to be done?