Sure, but then you still need a protocol between user agent and website. If you just do this in Javascript, you're not protected against phishing sites just forwarding the password entered directly.
Passkeys can in fact be backed by exactly this, i.e. a HMAC-only stateless implementation backed by a single password: https://github.com/lxgr/brainchain
Passkeys can in fact be backed by exactly this, i.e. a HMAC-only stateless implementation backed by a single password: https://github.com/lxgr/brainchain