Sounds like a regional niche thing.

I am capable of calling someone to pick me up, walk my bicycle to a nearby bike shop or walk it to work/home depending on where the flat occurs. The service you seek sounds like a good idea, but realistically, I think it would be faster for me to troubleshoot a solution myself. I live in an urban city with a cycling/commuter community, and don't think this kind of service is available in my area. it's possible it exists in NYC, European cities, or somewhere. But probably wiser to practice learning how to make your own repairs unfortunately.

I bought tires that have a tube within the tire ( I forgot what they are called) but perhaps speaking to your bike shop about getting different tires to prevent puncture is more realistic.

I have rode over glass and most of the time it didn't puncture with my tires. Only a couple times and I just had to replace the tube inside. I got a staple in the tire once and that punctured the inner air tube.

My friend has had fellow cyclists pull over to offer them help, but I was not so lucky.