Users who truly need that ability can create multiple certificates, and synchronise them as appropriate.
you:
> A single per-user client certificate is a cleaner solution, without the vendor lock in problem, since there’s no need for real time synchronisation of an evolving set of passkeys.
reply:
> Having a single certificate makes it trivial to implement cross-website tracking.
you:
> Users who truly need that ability can create multiple certificates, and synchronise them as appropriate.
well, indeed! perhaps designing a system to support multiple certificates with synchronisation, so that we're not forcing ever user to be trackable by every single website, would be a good idea.
some sort of keys to enable one's passage in to a website?
this is a cancer on this website, and certainly one I'm also suffering from, despite being quite aware of it - real life things are usually pretty complicated and just because I know enough to make a random guess at a solution, it doesn't mean people who have put way thought in to the problem have done a bad job or missed by brilliant insight.
Also, having a single cert shared across multiple hardware tokens is a security risk, as it becomes impossible to distinguish the tokens or revoke only a single one of them.