I think your argument is somewhat invalidated by your last sentence: the world for girl is generally seen as a standalone word, and so it seems odd.
Of course there is reason why is it so, but that is true for all oddities in every language: they made sense originally but as the new thing became the norm the origin of it is lost.
> the world for girl is generally seen as a standalone word, and so it seems odd.
That’s the thing: language also change the way you see things. Native English people might find it strange for the reason you mention, but German people can find it normal, because it is a diminutive following the usual rules. It is not a “standalone word”: it is a root and a suffix.
It is not an oddity at all within the framework of the language (which has its share of irregularities already).
I am not sure that it is seen as standalone. Surely, one doesn't use "Maid" or other archaic terms from which "Mädchen" is the derived word. But to me I am aware that its a diminutive. If I speak dialect I also use the dialectal diminutive (Mädle). Of course to someone learning the language that level of understanding is hard to reach without immersion for years.
Of course there is reason why is it so, but that is true for all oddities in every language: they made sense originally but as the new thing became the norm the origin of it is lost.