Your backups are the generated Authenticator backup codes. Most services give you anywhere between 5 and 10 of these, giving you 5 to 10 chances to log in without your stick. That's plenty of leeway.
No reason not to just revoke the old factor and buy a new one.
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.
No reason not to just revoke the old factor and buy a new one.