In this survey, 5.3% of girls 20 years or older watch mecha shows, while only 2.5% of boys in that age group do. So even if it’s marginal, it appears as if girls really do like watching giant robots rip each other apart. But most girls don’t watch it for the mecha themselves, but for the story, the world view, and the characters other than the mecha; but at least they are watching the shows, so that is all that counts.
This survey is not the end all, be all guide to the minds of Japanese girls, I believe a bigger sample is needed for that. Nevertheless, girls do like mecha, and that gives me hope for the future.
In any case, the beauty of, say, Jehuty transcends time, space, and gender.