Although I wholeheartedly agree with all the remarks regarding the total disdain of the U.S. DoD for nomenclature, I believe it is worth mentioning here that the A-37 designation itself must have seemed equally annoying to aviation enthusiasts when it appeared... Indeed, the "A-37" designation was simply carried over from the T-37 (the YA-37A was initially designated as YAT-37D). Still, since the A-37 had never been officially allocated in 1942 (after being tentatively reserved for the Hughes DX-2), it was not too shocking for the Dragonfly to take that spot.
Also, I can think of at least one equally annoying example of a reused designation in times past: when the B-26 "Marauder" was retired, and the A-for attack mission cancelled, the A-26 "Invader" became the B-26... only three years after the end of WW2, and while Marauders were still called B-26 in foreign countries that still used them.
But yes, I agree, while those were isolated examples, the trend nowadays seems to be that such nonsense has become the rule.