The problem with this is the backup codes are different for each service. With one service, I can keep a backup card in my wallet, another in my house, and another at somebody else's house in a different city, giving me very high assurance of availability in the event of token loss or destruction. I can't maintain that level of backup for every service I sign up for.

Even multiple tokens isn't a good solution for lots of services, since you need possession of the token to enroll.