To cut the foam out you need to take the tyre off... not really a roadside option. I have enough practice fixing punctures on some of my farm stuff and taking land rover size tyres off and on with tyre irons is a pain. I’ve have a few punctures fixed locally and, yes, they just cut a section of foam out and fit a mushroom. Roadside plugging on/off the car just from the outside should get one home, but I'm at an age where crawling around the car to do stuff is painful and certainly not a motorway hard shoulder thing to do. My solution is an RAC membership (covers the other cars too) and carry drinks and snacks and be patient.I think you are right and for anyone comfortable doing that it is probably worth it as an option. Just cut out the section of foam around the puncture area.
For me, I had a couple of situations in previous cars when the tyre was totally irreparable, so I was very glad of a spare to get me and the car home at night. I did ponder about getting a spare for a while, but having got it I am now very happy about it and with no negatives to report. Even for those who use breakdown cover for a puncture, totally understandable, then having the spare just simplifies that process as well.