There are lots of comments in this and other blogs about slime and its use. Grab a cup o’ joe and graze through them at your leisure although I think the bottom line is that most eschew the use of slime because of its effects on the tire pressure monitors.
As to the 12v compressor however, that’s a pretty universally accepted good idea. It can help significantly for a slow leak to get you somewhere more convenient, it can reinflate a tire that you’ve repaired yourself with a plug kit, etc., etc. No real downside other than the space it occupies in the f/trunk and initial cost. My choice was a Dewalt 20v inflator since I have a few of the 20v batteries from other Dewalt tools, it also connects to the 12v cigarette socket in the car, and with an adapter can also be powered by 120vac. It’s strong, portable, and comes with attachments to inflate tires, balloons, mattresses, etc. For details:
Dewalt Tire Inflator.