A TLS client does not contain any trusted private key. You can write one yourself by reading the RFCs. The same is not true for WEI.
The other provides the website the ability to ensure that the user's device is one of an approved set of devices, with an approved set of operating system builds, with an approved set of browsers.
These are fundamentally different, surely you can see that.
> similarly both can be avoided if you're willing to not participate.
Actually, no. Unless your definition of "avoided" is simply not using a website which requires attestation, which, over time, could become most of them
In WEI, the users (the ones being attested) _cannot_ avoid WEI. If a website decides to not allow an unattested user, they can simply decide to refuse access.
The EV certs still exists, but the browsers don't really differenciate between DV and EV certs anymore.
But TLS certificates solve a much narrower problem than WEI ("are you communicating with the site you think you are") and are widely and cheaply available from multiple organizationally independent certificate authorities.
In particular, TLS certificates don't try to make an assertion about the website visited, i.e. "this site is operated by honest people, not scammers". WEI does, with the assertion being something like "this browser will not allow injecting scripts or blocking elements".