Fun thing about small claims (once had to sue a bad landlord, eventually settled out of court), even if you win you have to extract payment. That means you need to figure out which banks have which accounts you want to garnish and contact them, which properties to put liens on, etc or hire a collections firm to do that.
I suppose an institution might be more willing to just pay up and be done with it, but if they want to make it costly they very much can, even if the judge immediately sides with you. Often negates what you would have "won", particularly if you factor in time.
"Could" is the operative word, just as likely you'll end up exchanging one form of time/money/stress for another. If you want the satisfaction that your money went to the courts/lawyers/collection's agencies rather than the entity who wronged you, fine, but that's about the best you can hope for below a certain dollar amount.
Also you have to prove damages, back when we were suing the landlord I brought up throwing on lost wages for the time I had to take off work to deal with the illegal stuff we were suing over, and our lawyer said "yeah we can try but it's unlikely the judge will award that because you weren't forced to take that time off". There's all sorts of gotchas like that.
That experience really opened my eyes to how the system really does screw the average person. I'm upper middle class and extremely well educated, so is the rest of my family who were supporting us throughout. I can't imagine how someone making the median salary who reads at a 5th grade level would navigate it. That's probably what said scummy landlord was counting on and why he settled when it was clear we weren't easy targets.
The system serves the common man reluctantly at best. Justice is a luxury good.
Why is small claims court better than a law flipping the default liability?
It's basically insane that we require individuals to sign a blanket billing authorization prior to receiving care. Perhaps the hospital should have to provide a maximum amount that is at risk (hopefully creating pressure to operate in a sensible way).
And what voter would ever want things to be this way? What constituent, rich or poor, conservative or liberal, says "ya know, I like paying for healthcare even when I have insurance and I'm going to keep voting for the one who keeps this status quo!" ?
Some very clever people have architectected an effective scam to prevent the democratic system from solving this. And I'm not referring to a republicans vs democrats debate about free socialized care vs hands off privatization. I'm talking about little steps that chip away at the problem like the one you described. Or forcing them to pay first, and only later have a debate about it. Or holding insurance liable for injury resulting from denying coverage. There is plenty of room for improvement and yet the representatives manage to accomplish nothing along these lines.
I suppose an institution might be more willing to just pay up and be done with it, but if they want to make it costly they very much can, even if the judge immediately sides with you. Often negates what you would have "won", particularly if you factor in time.