You display the issue simpler than it is. This problem exists in German as well, for example in law you often write things like: "The actor/actress who uses his/her ..." (except for laws dealing with maternity). And we infrequently discuss simmilar issues like those in earlier comments (for example the German word for university student is "Student" but this is also the male form, so a gender neutral form "Studierender" is often used, although this is strictly speaking not the same).
And as a side note, not all genders are "random" in German. For example the neutral gender of maiden you used in your quote is actually based on a rule. In German words ending with "chen" are denoting small things of something usually "larger", e.g. Brot -> Brötchen (bread -> rolls). Those words are always neutral, independent of the gender of the originating word. The confusing issue here is that girls are small woman (the old, no longer used word in German was "maid") but boys are not called small man. Maybe the inventor of German language did not know if boys really where small man, while he was sure for woman :-))