That's part of the horrible experience I hate. why should I have to have my phone to login on my computer.

You only do it if you want to. You can put your passkey in keepassxc or 1password or bitwarden or google's password vault or any other cross-platform passkey platform.

It's only a problem if you pick a platform that locks you out, even then there's workarounds. It's not a replacement for logging in every day, it's more a replacement for typing over the 64 character random password from your phone's password manager on the library computer.