This is not designed to prevent adults from coöperating with minors; that makes no sense as a design goal because any technical measure can always be bypassed with “download this for me and give me the file”. This is designed to prevent minors from being able to access systems without an adult.
Nothing prevents an adult from buying alcohol on behalf of minors; that doesn’t mean laws that prevent minors from directly buying alcohol are useless.
If the proof of adulthood scheme is truly anonymous, one adult with some technical chops who thinks "kids should be allowed to watch porn if they want" would be able to, say, run an adult-o-matic-9000 TOR hidden service that anyone can use to pinky promise that they are an adult without fear of repercussions. If such a service comes with a meaningful risk of being identified and punished, it is by definition not anonymous.
I suppose I'm just not convinced giving up some basic liberties for a law that converts into sternly worded advice if just one adult chooses to break it is a great idea.
I also don't think you'll find many ISPs terribly keen to fight for the neutral treatment of TOR connections when the reason for this fight is explicitly to serve porn to minors.
For example, in the UK it’s only illegal to give alcohol to a child younger than 5 years old.
France has no limitations, giving a toddler wine is not explicitly illegal. Getting a child drunk would be.
Multiple accounts must be supported, because e.g. personal and work accounts must be separate to not mix them.
The certificates in question can use a few mitigations: short lived, hardware stored (in a TPM, making distribution harder), be single use, have a random id which the service being accessed can check how many times has been used.
> but then the issuing government and the service providers have a timing side-channel they can use to correlate identities
That's not reallya concern, IMO. That would always exist as a risk - most people would probably have a flow of trying to do something, having to prove ID/age, doing that step, continuing with the something, which means you'd probably be able to time correlate the two sides quite often. The solution here is legal with strong barriers, not technical.