What nobody seems to consider is the entire point behind registration.
The point behind registration is, 99% of the time, related to taxation.
The traders at the Starport don't care about the ship, they care about the goods.
The Immigration/Border Control officers don't care about the ship, they care about you -- the traveller.
Law Enforcement might care about the ship (since it might be stolen), and registration is a fine way to check that, but it's not the primary task.
The taxing authorities, they care. They want their fees paid.
I don't even know if ships will be taxed (much like cars are taxed today), since there's no real public infrastructure to support vs simply charging docking fees -- at which point the Starport really could care less about what the ship is, as long as the slip fee is paid up.
But maybe there's an Imperial tax on ships (not shipping) Because They Can.
However, consider, that currently, here on Earth, in the US, at least in California, Law Enforcement is not used to prosecute repossessions. They prosecute theft, which is different from an unpaid payment, and repossession is delegated to private companies.
Currently authorities run vehicle registration because they can, it's cheap. Do they check VINs? Only if you're getting cited. Do they check engine numbers? Chassis numbers? Almost never. It's inconvenient and almost never called for. If they're getting to that level, you're already in so much trouble it probably doesn't matter one way or the other how legit the matching of these numbers is.
The cheap stuff they'll do routinely, more invasive stuff is left to the CSI folks.
So, the standard transponder aka "starship license plate" fits the role pretty well without having to drag out densitometers and tri-corders.