Ball bearings aren’t wheels to me though.

For me, a characteristic feature of a wheel is that it is circular, not spherical. Which would disqualify ball bearings.

Doors are harder to define though. Since there can be doors for non-people. For example dog doors.

I would define doors as “manmade object that sits between an ‘inside’ and ‘outside’ which can be closed or opened. And has the main purpose of letting things in or keeping them out”. But for that you’d have to define “inside” and “outside”. And would include windows, since they let air and light in and can be closed. I wouldn’t consider a window a door.