This is a real problem. You can't backup Google Authenticator for security reasons.

Websites are supposed to have a way for you to get back in if you lose your 2FA device. Currently, many BTC websites don't have a way to get back in.

You should check how you can get back into your account if you lose your 2FA device for each website you use.

If there isn't any way, disable 2FA and re-enable it, and when the 2FA QR code appears, take a photo of it and keep it in a safe place. This is much less secure, but it is better than getting locked out.