This is not a Google product, it's an initiative by the so called FIDO alliance [0]. You need some kind of secure backup for the private keys, which Google, Apple, Microsoft etc. already offer as part of their account system.

Regarding the need for a mobile device: I guess it technically wouldn't need to be a mobile phone, but that is the easiest way to get biometric authentication and a secure enclave. This is how passkeys work. Don't like it, don't use it. It will probably take quite some time before services offer passkeys as their only authentication mechanism.

[0]https://fidoalliance.org/members/