Just a thought about the 'A' sizes, I
think it may have something to do with the fact that you can get AAA as the lowest size and since A cups are at the lower end of the range it's probably just easier to have a single letter as the main principal size. It's a bit like batteries, you get AAA, then AA which is bigger.

Doesn't explain D and DD though.
Just read this:
"Some manufacturers use size DD but then continue with E, F, G, H, I, J, etc. Others use DDD to represent an E and some go on to use E, EE, F, FF, G, GG, H, HH, etc. This can make purchasing a large-cup bra difficult."
I suspect it's just so manufacturers can produce a wider range of fittings and thus satisfy their customers. So they could have a line where DD is larger than a D but smaller than an E, rather than DD being the equivalent of an E.