I guarantee you that EMTs definitely do NOT typically have very good health insurance, speaking as someone who has worked as one for multiple companies and as an educator in EMS in this region.
If you're talking fire department-based EMTs, then yes, but these make up a significant minority of EMTs who are often running on minimum wage and often given the bare minimum of health insurance.
Well, I mean they should - they're highly skilled and paid a lot of time and $ in education and training. And these things are relative: they're specialized and require more training that many other positions - more so than drivers.
If they're going to be paid less, they need to be compensated elsewhere.
I would not consider a basic "EMT" highly skilled. Maybe a paramedic, then yes, but not an EMT. However if you're referring to residents than yes they would be considered a lot more skilled.
It doesn't take much schooling to become an "EMT". However with what they have to deal with and how essential the services are, they definitely should get paid more fairly.