The case of «das Mädchen» is a mere historical curiosity and doesn't require the memorisation as long as long the person in question is acquainted with basics of the German noun formation, i.e. the "-chen" suffix in German, when added to a noun of masculine or feminine gender, unequivocally results in the "neutralisation" of the noun gender, as well as the "umlautisation" of the stressed vowel of the noun being gender bent, eg. der Hund + "-chen" -> das Hündchen. It's a very simple rule, really.

The thing about this, though, is that it only works if you get lucky and none of your nouns share a gender. I feel like that undermines the argument at least a bit.

I feel like I could come up with some examples if I had kept up with German after high school. I remember it being difficult for a year or two, then it seemed more helpful as we got into more complex language mechanics. In any case, German felt more consistent than English, and most of the words just felt right with one gender or another (and in speech you could usually get away with something between "the" and "duh" if you weren't sure about der/die/das).

They are generally going to sound good together because the word and the pronoun co-evolved. If they didn't sound good together, either the pronoun or the word would have changed. That isn't about the gender being right so much as just the sound, though.

There are other possibilities, but trying to apply logical rules seems pointless; the whole point of language -- what actually makes something a language -- is a completely arbitrary set of rules.

If you do that in German (i.e., "Ich habe eine Tastatur und einen Stein. Sie ist groß und er ist grau."), everyone would start slapping you with a style manual. It's just so unnecessarily contrived.

The major argument for keeping gendered nouns as they are in existing languages is that speakers would be uncomfortable with having their language changed by some standards body.

German isn't my mother tongue, but I think it's a form of diminutive, which often becomes neuter in Germanic languages, as for instance in Dutch.

I agree it feels silly to learn the gender of "sexless" words; but this case and the rule behind it are quite clear in the respective languages this occurs in. I guess it's not unlike English using neuter for animal pronouns, which feels strange to speakers of most Germanic languages.

What is an animal pronoun?