One thing about the US, is how we handle settings where one could conceptualize a contract as being needed, but where it would be way too inefficient and impractical to negotiate, write out, understand, and sign, a written contract. In those cases, which includes things like retail sales, restaurants, and may other cases, the UCC or Uniform Commercial Code[1][2] applies. Not sure offhand if that relates to the medical example or not, but I expect that at least some similar notion applies. So there are binding laws that cover these transactions, it's just not done the same way as a "full fledged contract".

[1]: https://en.wikipedia.org/wiki/Uniform_Commercial_Code

[2]: The UCC also covers other things, but these cases are a lot of what it's best known for.

Knowing medical prices up front would be entirely possible and practical. In most situations, you should be able to sign contract up front.

It is also illegal in USA, although that only changed recently.