> The UK's current system is realistically about the same age as the US

no, it's evolved continuously from 1066

by the time of the US rebellion, the king was already neutered

> their first PM was in the 18th century.

the title of "Prime Minister" is a modern invention (and not a formal position)

there has been a Lord High Treasurer since the 1100s

a constitutionally limited monarchy is older than the US

meanwhile the modern US seems to be a absolute monarchy that isn't constitutionally limited