This is why insurance plans have out of pocket maximums. To prevent this exact issue.
We can say whether those maximums are still too high (some really are), but the mechanism is there.
The real issue is that most people don't have a rainy day fund to deal with such emergencies. And that they are too expensive anyway.
There are 2 concepts you should always keep in mind.
1. Always avoid the hospital unless you are literally dying. Surgery centers are owned by doctors who will negotiate a fixed fee, because there's someone to negotiate with (unlike Hospitals which run on the CYA principle). Also, most doctors can do procedures in office, if they have the right one.
2. Medical debt will never lead to collections. Hospitals may sue you, depending on the state, but that carriers reputational risk. A good PR push and a decent lawyer to threaten discovery will be enough to fend off even the most aggressive hospitals - this allow you to setle at a very reasonable price vs what insurance would normally pay.