I mean, in theory sure… sometimes… particularly with alliteration. It could be.
But that’s not really the case here because most of the names aren’t alliterative or even simpler. In several situations (Superman/boy, Supergirl/woman, Spider-woman/girl, Batgirl/woman, Wonderwoman/girl), both versions exist.
But the primary reason is historic. The convention was set in a time where the diminutive female form (girl) was far less controversial than it is today. There are lots of versions where the diminutive was replaced by the mature version later to comply with cultural norms (Invisible Woman, Hawkwoman — though this has sense reverted in most instances). And the point is the percentage difference with male diminutives is statistically significant even with assumptions of phonetic preference. That’s why her regression analysis is important.
In any case, it’s entirely intentional Batgirl is probably the best example. Batwoman actually predates the character. Followed by a different character of Bat-girl that is unrelated to the character most people think of. THEN both of these characters were retired… Then they brought in the Barbara Gordon Batgirl character and specifically made sure she was girl and not woman so as not to upstage Batman. She similarly had other limitations, like expressly being a brown belt rather than a black belt, specifically so the readers knew he or Robin could beat her up in a fight if it ever came to it.