Although this is good, all it saves is typing a few digits and checking a box "[ ] let's not do this again on this particular computer".

Other hardware solutions could be found. For instance, an app on the phone could receive a security token string, and use bluetooth to send it to the PC. Or, a QR code (or bar code) could be sent to the phone which pops up on the screen. This is held up to the PC's web cam which scans it. [Insert your idea below.]