Not sure what's happening because I personally don't use Coinbase, but 2-factor authentication is mostly required by financial services to increase more security for their users and to prevent hackers/scammers from accessing their accounts and stealing their money.
Why did you "destroy" your authentication keys in the first place(or did it get destroyed unintentionally)? Knowing that Coinbase would require it every time.
I had an Android problem where after a phone reboot some apps were being deleted. After googling around I saw that some others were reporting the same thing. I got tired of having reinstall 4 - 5 apps every time I restarted the phone. So I took a backup. The next time I rebooted my phone and apps were deleted I just did a restore from the backup. For some reason my Google Authenticator codes never worked again. Somehow they were damaged during this process.
I had moved my funds from Coinbase Pro to BlockFi to take advantage of the interest they pay for deposited bitcoin. Since that bitcoin movement I have not had occasion to again buy/sell/transfer any bitcoin using BlockFi. I have been able to sign on/off BlockFi, but I would probably have had a problem if I actually tried executing a transaction. I have initiated the process of getting re-authenticated (or whatever the term is) at the following site:
https://help.blockfi.com/hc/en-us/articles/360048862652-I-lost-my-2FA-Code-how-can-I-access-my-account-again-However I still don't quite understand the Coinbase stuff. They sent me a code to use to sign on, and an email to verify the device I use to access my account. But wouldn't I expect to be asked for an Authenticator code if I tried to execute a transaction? I don't see how it would now recognize my Authenticator codes. I don't know anything I did that would allow it to.