UNLESS you have many cars and spend ALOT of time fixing them often (unlikely) OR you do alot of repairs for other people (also unlikely), you don't need an air compressor or air tools.
I've been an auto tech for over 25 yrs and I've never had an air compressor or any air tools at home, not even in years past when I'd do occasional side jobs and had 5 of my own cars at one time.
I DO have a nice electric impact which occasionally comes in handy if I ever need to remove wheels, like put my mounted snow tires on (any day now). Most other repairs at home don't need the added speed of air tools and I'm never in a big hurry at home.