My government's e-signing web application (which stores private keys on the vendor's servers for all citizens, but that's another story) already does that.
It used to not even accept Yubikeys, only a fairly unknown other brand; now they finally do support Yubikeys, but only the "FIDO L2" certified kind, i.e. the FIDO and "security key" models, but not the most common plain Yubikey ones...