Then, online accounts could query the device and see if there's a key that matches what was made when they setup the account or added 2FA. Each account could have its own key, associated with the owner's master key, and it'd have to match the one on file - something like that.
I imagine it's have to be standardized and easy for site owners to implement. I guess it could also be done at some central location using something like OAuth, though individual sites should be able to add it - and fairly easily, and for just the cost of learning to add it. Maybe make it fairly simply, as easy as LetsEncrypt - or even easier.
Now, in my head, they'd enter their username (no password yet) and that's when the check would be performed. The site would request the token from the USB and the USB would request the token from the site. If the two match whatever criteria the security gurus come up with, they are prompted to enter their password. I suppose there could be additional checks and maybe even periodic poling from either the USB or the site.
Because the phishing site wouldn't have the correct key, it would fail and the user wouldn't even be asked for their password. Ideally, the user wouldn't have t do much more than carry their USB drive with them.
I suppose it should be easy for the owner to clone the USB key. It should also require some sort of master password to even authorize it to hand out keys. I imagine enterprises can lock them down to a key and a workstation, meaning that they can can only work in certain computers and certain computers will only accept one physical key.
I am sure this can be refined and monetized. Selling solutions to businesses and services would be nice. Recovery should be possible but difficult. I'm sure it can be layered with additional features. It should probably be optional, and not mandated by law for the general population and for personal computing - but available for them.
I'm sure there are ways one can think of to get by it but it does seem like it'd be a good place to start. It also doesn't seem like it'd be technologically difficult to accomplish, or even necessarily expensive.