A client cert can be stored, so it provides at least a little bit of identification certainty. It's very hard to steal or impersonate a specific client cert, so the site has a high likelihood of knowing you're the same person you were when you connected before (even though the initial connection may very well not have ID'd the correct person!). That has value.

But it also doesn't involve any particular trust in the CA either. Lets Encrypt has nothing to offer here so there's no reason for them to try to make promises.