Modern letter forms are the product of a combination of tradition, technical considerations, readability considerations, and interactions between handwriting and printed texts as well as between several flavours of the latin alphabet (roman type, blackletter and gaelic). Therefore I doubt that anybody can make more than educated guesses as to why certain variants survived while others didn’t. After all, there isn’t any committee that decides things like that only a single form of the letter d shall be used.
Anyway, here are my educated guesses:
As a general tendency, we experienced a strong homogenisation of letter forms in the last centuries. This was probably stimulated by the industrial revolution, globalisation, an increased alphabetisation and the related advent of printed type as a product for the masses. This probably ends with the digital revolution, which made it tremendously easier to use different typefaces and letter variants – however, only time can tell whether this is actually the case.
Now, why did certain variants survive?
I presume that two variants of a and g mainly survived, because the two-storey variants are not feasible in handwriting, while they have advantages in print: The two-storey a is easier to distinguish from the letter o; the two-storey g is narrower and also easier to distinguish due to its unique shape.
I presume that so many forms of the ampersand survived because the same processes that lead to a homogenisation of type also lead to a drastically diminished use of the ampersand: Instead of being a common shorthand for and, it was only used in titles, logos and similar and almost completely disappeared from regular text. Therefore considerations of space and readability were much less important, and æsthetics could prevail, favouring various and creative forms. Moreover, it’s in the nature of the ampersand that it is a standalone character that is not embedded in words, and thus coherence with other characters is much less of an issue. Thus the ampersand became the one character where type designers could let their creativity run wild, and it still is (with the exception of coding typefaces).
Something comparable happened to capital letter Q, as it is rather rare and almost only occurs in the sequence Qu in most languages: