I also don't use my personal key for work stuff and recovering my work key is my sysadmins problem :)
That said, when I had admin accounts at work, we used TOTP with a similar scheme: when we registered important (admin) accounts we shared the second factor (the QR code) between 2 people and sometimes I printed the QR code itself. This works for AWS, gsuite, github, etc. I still receive calls from old colleges for TOTP codes occasionally :)
What about steganography in tattoos? That would be pretty interesting. Perhaps combining that data with a short code or seed that you memorize.
The tech exists. My neighbor works for a company that does encoding of data on packaging. Goal is that every cereal box on the grocery aisle can be individually tracked.
I think a good with system should include some sort of revocation, like a master key you can keep in a safe to revoke other devices.
But I'm thinking of a revocation scenario, where a key is stolen. In that case the attacker can just remove your keys first.
If the hacker gets your key, and your password it's game over.
But hacking the password will take some time hopefully, and systems usually have retry limits etc. so if you discover your lost key, you hopefully have some time to revoke the lost key.
I personally would not use it for password-less login, as it is only good as a second factor.
If your threat model includes any real likelihood of people capable of stealing your keys and cracking your passwords, then 2FA is only a small part of the opsec you need.
Things like NSA's Zero Trust Security model comes to mind https://news.ycombinator.com/item?id=26549363
If you're at that level, you probably need specialist infra.
But potential compromises don't mean you're not less secure than before, Yubikey would still make you more difficult to hack.
By enrolling my spouse and cross registering all keys, both of us are safe. We might loose our keychain, but we will always find each other, even when we are traveling.
This works for Google and GitHub, but not every service allows for multiple keys. But this should be a no-brainer imho.