Backup codes and then the protection is against illegal SMS porting which is a social engineering attack hard to otherwise defeat. Your phone is fulfilling a different function and yes it does collapse both factors onto one device but the primary risk wasn't loss of phone, it was weak password and no variant second factor and then porting attacks on SMS.
I didn't understand the point your are making. I'm referring to the overall attack surface area of apps like 1password (which I think also have browser extensions ?). TOTP is better than sms, but why put it in the same app as your password ?
You have to ask yourself what's the primary threat. Yes,the point in strong sense of a second factor is a fully independent test. But the actual threat it mostly protects against is credentials threats. Not loss of devices or compromise of a keystore. SMS as second factor is way way worse because of the porting problem. Otp inside 1password is a compromise but it protects against the primary threat.
If you crypt your disk and use a good passphrase or a long pin and passphrase on a phone you are not that badly exposed.
I'm now using OTP Auth in iOS, which allows backing up the codes. For me the risks in that are worth being able to easily restore my codes.