I don’t think you understand how the system works. Or perhaps you do, but fantasize that reality were different.

First, in a non-urgent situation, you’re going to be asked about payment prior to service, and they may refuse to treat you if you can’t pay.

Second, in an emergency situation where you’re unable to provide affirmative assent, you’ll be liable for costs under the doctrine of quantum meruit (quasi-contract). If you don’t pay, the provider can sue you, in which case, the court may force you to pay on their terms.