I understand what you are saying, but the fundamental difference here is that for PKI, the browser has to be configured properly as your key pair must exist and

I understand what you are saying, but the fundamental difference here is that for PKI, the browser has to be configured properly as your key pair must exist and the correct public certificate must be used in TLS negotiation. The advantage here is that the password can be copy and pasted into a password form after TLS has been negotiated. Coupling authentication with encryption has its place, but I would think that it would work better when accessing a service through an app rather than a browser since the app publisher can create unique a key pair and sign the certificate with their own CA and use that for authentication, but in the context of a web app accessed through the browser copy-and-paste beats having to configure your client certificate per domain at least from a "user friction" point of view.