Going to the E.R. is a hellish experience unless there is something very seriously wrong with you.
People with gunshot wounds, knife wounds, heart attacks, compound fractures, stokes, having babies, etc., always come first.
I guess if you like sitting for hours in a crowded waiting room, maybe sitting next to someone who hasn't bathed for years, listening to people screaming in pain or yelling obscenities is your thing, go for it.
Fortunately, the last time I went to the ER I was so messed up I hardly remember any of it. (At the end of it all I owed the hospital about $10,000 to cover what my insurance hadn't paid.)
I've also taken people to the ER and that's never any fun.
Med accounts like you suggest are not a good idea. People will keep the money and not seek care for the sorts of seemingly minor complaints that turn into medical catastrophes. Many cancers are a good example of this. Catch them early and the prognosis is good and the costs not outrageous. Put off having a doctor examine them because you don't want to pay for the visit, then treatment becomes incredibly expensive and maybe you die.