Webauthn should allow use of private key authentication stored on external hardware key or in device.

You really want support for key authentication just like ssh.

You shouldn’t move private keys between devices, you should have easy way to add new public keys to a service when you setu new device.

Problem is permacookies or private keys don’t really allow ad-hoc access but maybe nowadays people don’t need to login to their accounts from cyber cafes :)