> and force the states to agree on a set of standards that apply across the country

To rephrase, you're asking that the same license plate work across all of the European Union.

To realize why this is unrealistic, one has to go back to history and understand the core concept of the United States of America. It's right there in the name itself. It was a compromise to unite and bring agreement across all these disparate states that were in their very own right entire countries (and most, even till date, most states in the US continue to be larger, geographically than most countries in the world), agree on some very basic terms so there could be trade across them, kind of like the European Union.

> but this current system is Kafkaesque

Of course, this license plate registration thing was optimized for tax and fee collection, and it does that job very well. All it takes is for someone to run for office and say they're going to overturn it all.