Credit cards are already a privacy catastrophe for anything where you have to pay money, but people will push back if you demand one for anything where you're not supposed to be paying anything because people are rightly wary of being charged when they ought not to be. Anyone who gives their credit card number for a "free trial" learns that the hard way and then becomes appropriately cynical.

A state-issued ID generally doesn't work over the internet, which is good. Some of them can be read electronically in person, which is already being abused to a limited extent and should be gotten rid of.

Which is the general response to your concern: "This is already a problem" means we need to go the other way and address that so that doesn't happen anymore, not intensify the problem and set it in concrete so it can never be fixed.

Centralized identity is a design flaw. Your bank needs to know if you're authorized to withdraw from your account, which is why you have a bank card. Your email provider needs to know if you're allowed to access your email account, which is why you have an email password. Your apartment building needs to know if you're authorized to enter, which is why you have an access card. What we don't need, and should not have, is a single primary key binding all of these things together so it can be correlated in a single database.