Yep, all the things you mention are effectively contracts (in the broad sense) where both parties commit to previously agreed upon terms.

It's for this reason that most countries have some kind of mandatory insurance against emergency medical treatment where the person being treated basically has no choice (even if they're conscious) and is thus incapable of forming a valid contract.

You're right that in this scenario it's weird to expect someone to still pay for their treatment, but if you can't force people to be fully insured against such costs you need to force them to pay for costs they couldn't freely consent to.