I'm not sure that there should be a system that requires US citizens to carry a credential, or require them to to have a single vaccination credential. I believe what people want is just a document/form that would show they had the vaccine for whatever purpose the individual needs it for. Much like the "old fashioned" yellow immunization record that many of us have.
Sure. And that wasn't abnormal. But people are going much further than that with this.
Thing is, in the past you had exemptions. People were able to have a religious exemption. Or finding a doctor out there that would write something that you shouldn't get them wasn't all that hard. Some states even allowed exemptions for personal reasons. So there was really no reason to create phony vaccination records.
But now that we are very seriously talking about denying goods and services, and even possibly people having to lose their jobs, if they don't vaccinate, I think you'll see a huge uptick in phony records. And without the government issuing the credentials, there will be verification problems.