WebAuthn is only secure because it entrusts to browser to pass verified domains to your USB key. Why can't SQRL just do that with no other protocol modifications? Then we don't trust the user with anything, protocol-wise. Cause sure, if the site can pass a QR code or URL directly everytime, that's an issue because you're still trusting the user to manually verify the domain, but if the interaction is mitigated by a trusted party (i.e. the browser), then I don't see the problem.
Technically the FIDO device ("USB key") doesn't get told the domain name. The browser throws it into a compression function with the random values and a bunch of other stuff to compute a value the server also will be able to calculate for itself. Your key has no idea what facebook.com is, doesn't care.
The FIDO device is impressively dumb on purpose, makes it hard to attack. Given an input and a hardware user interaction it responds, cheap ones aren't storing anything or doing any conditional work, and the interaction means you can't do any sort of brute force attack - if you somehow RCE the browser and prompt the user "please press the button a million times" they're going to report that as a bug and close the browser.
