IMO plugs are more of a field repair thing. Usually mga off-roaders / overlanders gumagamit since they'd often have air compressors on their rigs, but it can be useful even for cars, especially the sporty ones that don't even carry a spare.

I think there's a picture somewhere of a Porsche that ****ed up his brake calipers because the owner fitted a spare that did not properly clear the brakes. Carrying a couple of plugs and a small air compressor could have gotten him back on the road with a lot less grief.

In a shop where the wheel can be properly dismounted I'd always choose a patch over a plug.