What IDs are you referring to and what’s the headache? Presumably one ID is a passport. From your first sentence, I would assume the second ID is a social security number, but how does it become “out of sync” with a passport?
Get a passport as a minor, change your name as an adult, realize SSA has your wrong bday, descend into bureaucracy hell as now both name and DOB don’t match.
While I am sure the bureaucracy surrounding such discrepancies is enormous, I’m not for sure I understand how it relates to a discussion about national IDs. A passport is effectively an optional national ID, so none of these issues would be solved by a national ID.
The Social Security Administration (SSA) issues IDs at the federal level, which are applied for using state or county issued birth certificates (as well as other ways). They sometimes make clerical errors. Those errors can propagate into other federal identity databases, such as the taxpayer record system operated by the Internal Revenue Service or the passport database operated by the Department of State.
The linkages between these systems are fragile or nonexistent, and if you are not careful about manually propagating changes between them you can end up in an inconsistent state which requires court action to rectify.
Passports are often used in lieu of social security cards because people are (correctly!) leery about using their SSN directly. I know people who have no intention of traveling internationally who have gotten passports because it’s extremely convenient to have a federally issued photo id.
I have neglected to get my state's real ID since it requires me to go into a location, which are soul sucking. Luckily, my global entry card is a Real ID. It only took two years to get that one. And when I had to go in for that ID, they didn't even check my driver's license or passport for ID. They just took my picture and that was it. Pretty poor due diligence.
Funnily enough I was able to fly without an ID when I lost my license--which was surprisingly hassle-free. But I had a hell of a time checking into my hotel.
You haven’t needed it since it’s such a bad ID that if you know the number you often don’t need to possess the paper.
You can also use a birth certificate to establish right to work, so yeah it wouldn’t be required.
Of course now I just use my passport, but like many Americans I didn’t have one for many years.
Eventually I was able to track down the underlying laws that the relevant rules were based on and call the head office in Charleston who put things right, but who knows what would've happened had I not been a native English speaker.
Some of this may have changed, it looks like "8 FAM 403.1-4(D)" would've been the rule that I needed back when I did this, and it does not appear to be currently classified, but lots of other rules still are. Point is, it may not be as simple as you'd think to "just" get a new passport.