From talking to other medics, I see that most of us carry simple useful tools, such as a cloth triangle, everywhere we go. And we're well-versed in improvising.
https://en.wikipedia.org/wiki/Good_Samaritan_law#United_Stat...
Virginia's Good Samaritan law: https://law.lis.virginia.gov/vacode/title8.01/chapter3/secti...
Do note that the licensing is done at the state level, so there are 50+ similar standards, not just one.
Most first-world countries are not obsessed with self-elevation and interest resulting from their own infrastructure breaking down
Third-world countries might be more the incubator you're hoping for but they generally don't care what happens to the non wealthy (and the wealthy's FO plans there as with everywhere don't involve looting cars on interstates)
So if I were to guess, I'd go with no, no "other countries have tried this out".
E.g. in much of Europe you're not getting a driving licence without passing a first aid+CPR course, and every car must have a first aid kit and a fire extinguisher.
Also, I recall that USSR had mandatory civil defence courses in universities - so everyone with a college degree, no matter if it's medicine or math, will have had a full semester of disaster followup & related issues; didn't USA have something similar during the cold war?
Medical training varies from team to team, but a minimum of wilderness first aid is pretty typical. EMT is pretty popular too.