Thats how it should be done, except in the US there is no way to check against a national database of IDs, not even on the state level with DMVs. You literally trust the plastic card the person shows you and thats where the problems start. Online its even worse.
However, most of those scenarios have the added security that the CC or some necessary confirmation letter to sign is sent to the registered address of that id. So you'd also have to stalk my mailbox to actually get the credit card. This actually happens - so people use locked mail boxes to protect against this.
That is, even for this "manual" id method, there is 2fa in the form of regular mail, made possible by the fact that you can't use my id and give them your street address. When you show my id - they immediately know what address belongs to that id.
The major benefits compared to SSN authentication still are:
* It's a physical object, you have to be physically present to steal each one instead of getting a hundred million at a time.
* Most people would quickly notice that their card is gone, report it, and get it revoked. You only have between a few hours to a week to use it, not the next 50 years.
So no, I don't think there's any Equifax equivalent where a data leakage would enable stuff like this.