WebAuthn explicitly tells Relying Parties (ie web sites) to all do this. All the services I use which offer WebAuthn or its predecessor U2F support multiple named hardware tokens and I enroll at least my Yubico branded device and one more at such sites. For those I use from a phone, the phone itself is enrolled.

AWS is the counter-example which will be (indeed already has been in this HN comment tree) cited as proof sites don't all do this, I've tried asking if there are literally any others, and never received any ideas. I don't currently have an employer and I don't use AWS for personal projects.

It's pretty common for sites that actually care about authenticating you (so, Google but not your Bank, GitHub but not your mortgage lender) to provide you with single use bypass codes which they tell you to write down and keep somewhere safe.