Hence why the UK hasn't done it.
UK - Excuse me US, would you like to have a reciprocal agreement?
US - Errr, you'll have to ask each individual State.
UK - Well, in which case we'd need to get agreement with every single one. Get them to call us.
In the present times it would go different:
1. Belgium and Germany would just forward their US agreements to Brussels (EU).
2. EU would recognise them and they'd be valid EU wide.
No need for double work within EU framework. After all, any EU emissary is entitled to represent UK, in the absence of UK representation for that issue, by the same coin that UK citizens can resort to any EU embassy in the absence of a similar UK facility. When EU officially accepts the forwarded agreements, there is no reason for UK to disenfranchise them. How else did I (as so many others) get a bona-fide EU license from an American one. When I go to non EU countries, they accept it as an EU license for all purposes. Period.
By this token, US licenses are theoretically already valid everywhere in Europe, but ofcourse in a moot manner at the discretion of pencil pushers, and at your own peril. As such it's more an internal EU issue, rather than a UK-"each US state" issue. To be or not to be (an ally), that is the question.