A compressor is a good idea to have anyways. Even with a spare tire, you might find it underinflated when it's finally time to use it.
For a couple of nail issues I had, a DIY tire plug kit has been useful.
One of those issues happened during a car control clinic, when an allegedly old nail left my friend's tire due to tire flexing, so the tire was losing pressure by the minute. Put the car on my scissor jack, pumped some air, plugged the tire — the tire was fine for a few weeks after that, and then decided to just put new tires on.
A scissor jack is included with '22s, right?
I once needed a spare when renting a car in a rural area.
Admittedly it was a stupid idea to drive that fast on an unpaved "highway"
I hit a stone that was in my "lane" in a blind corner...
The impact was so severe that the inside of the wheel barrel reached the caliper (the car didn't have a BBK),
and the stone caused some cosmetic damage to the rocker panel.
That being said, having a spare tire is beneficial for the piece of mind.
Will I buy a spare tire for the '22? Maybe, but not certain.