I don't regret buying a cheapie air compressor, although many of the uses to which it is put are probably unrelated to car maintenance.
Yes, it's an easy way to inflate tyres with zero effort but slightly more faff than getting a foot pump out.
I have an air impact wrench that has got me out of jail on a number of occasions when I would have been stymied otherwise. Most recently it has removed a hub nut and a lambda sensor that weren't going anywhere without it. It cost me about £20 during one of Lidl's promotions. An electric one would have cost me more than it would have been worth spending and I use it so occasionally that it would have had a dead battery each time, etc...
I have a small disc cutter that has got into numerous places that an angle grinder wouldn't have touched for jobs that a Dremel wouldn't have been man enough for. Ditto a die grinder. Again, cost for these was minimal. I bought them in the hope that they'd come in handy one day and was glad I did.
I have an air nail gun that has been great for many non car related jobs. Again, an air powwered device was so cheap that it was a no-brainer, but an electric one wouldn't have been.
I use mine to pressurise my Eezibleed so I don't have to faff around getting a spare tyre out and deflating it to the required pressure, etc. Wouldn't justify a compressor in itself but saves valuable time.
I've used it a few times to pressurise cooling systems to find leaks. Not impossible with a foot pump, but less hassle with a compressor.
I use it to run an air powered beer pump for home brewing.
I am often asked to fix comupters, radios and other electronics for people. Most items are full of dust, cigarette smoke remnants and very unpleasant to work on until they have had a good blast of compressed air or, if seriously contaminated, a blasting with a spray gun filled with an alcohol and distilled water solution.
There are probably numerous other things I've used it for,. None on their own justified the cost of the compressor, but, put together, it's a no brainer for me. YMMV.
Stuff that consumes tons of air clearly won't work well on a toy compressor but for occasional use everything listed above was completely painless if interspersed with the odd tea break to allow the motor to cool.