EU is making somewhat similar deals with Canada and Japan who have joined the EU SAFE program.
But yes I agree UK has some unfortunate exceptionalist tendencies, some Brits think that commonwealth makes them an empire. At least they behave that way.
Also the commonality with other English speaking countries seem to make them think they are more important than they are, as being part of a club makes them special.
Exceptionalism was a major part of the thought process behind Brexit.