But only for unpredictable, irregular events. Anything else is uninsurable. If someone sells you "insurance" for wellness checkups[1], regular, scheduled screenings ... or tires on your car ... you can be absolutely assured that they are taking from you as much, or more, in premiums than the cost of those services.
What you are looking for is socialized, state sponsored medical care. There is no problem in looking for that and I make no value judgement here on that.
The first step would be to stop mischaracterizing this as "insurance". It's not. It can't be.
[1] Yes, certainly wellness checkups and things like them can be enormously economically beneficial for the provider since they spend up front preventative dollars instead of emergency, acute dollars later but it still doesn't change the fact that those are not underwriteable as they are regular, on-going expenses - very much like the tires on your car.