AWS not offering multiple 2FA keys is one of my biggest annoyances, its a service that I feel much have 2FA due to its ability to run up extreme bills, but I also cant setup a backup key in case of loss or failure.
It is a big annoyance but I think most places (once they're beyond a few engineers in size) use federated auth that support multiple keys (Okta, Active Directory, GSuite) for AWS access.
You can also use TOTP and store the secret in a password manager then protect that with hardware keys.
At $JOB-1 we solved this by building a virtual TOTP service that grabbed the MFA secret for a particular AWS account from our internal secrets tool (which itself required MFA and supported multiple users) and used it to generate codes.
You can also use TOTP and store the secret in a password manager then protect that with hardware keys.