alt Hacker NewsClient authentication with publicly-trusted (i.e. chaining to roots in one of the major 4 or 5 trust-store programs) is bad. It doesn't actually authenticate anything at all, and never has.
No-one that uses it is authenticating anything more than the other party has an internet connection and the ability, perhaps, to read. No part of the Subject DN or SAN is checked. It's just that it's 'easy' to rely on an existing trust-store rather than implement something secure using private PKI.
Some providers who 'require' public TLS certs for mTLS even specify specific products and CAs (OV, EV from specific CAs) not realising that both the CAs and the roots are going to rotate more frequently in future.
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.