The tool to mount a tire onto a wheel costs between $50 and $2500 dollars and is very large. The alternative - a spare wheel - is a kludge! Cars carry around an entire tire and wheel all the time in a special compartment because you can't expect people to mount tires themselves. Or modern cars spec run flat tires which come with a host of their own tradeoffs.

Which one inflates the new tires, the jack or the wrench?

The tire shop who mounted the tires on the wheels, or a simple bike pump.

But I thought changing the wheels was a simple process you could do at home with the tools provided with the car?

A bike pump and a tire shop aren't provided with the car. Hell, most don't come with jacks or a wrench either. Some won't even include a spare tire/wheel nowadays.

Repairs can be pretty easy when you pay someone else in a shop to do the hard part for you.

In my case, replacing my iPhone battery required no tools at all after I paid the Apple shop to mount the new battery in the phone.

money can be exchanged for goods and services?? you tell me this now??