I asked a talmid of R’ Moshe what he believes his Rebbe holds. He replied.
1: Making Bat Mitzvah affair in a shul. Assur.
2: Making a Bat Mitzvah affair, anywhere. Not likely to increase ones yiras shamayim, why bother. Then again, he says the same about Bar Mitzvah affairs as well.
I cant say this is true of all, or even many, girls schools, but I know of one girls school in Brooklyn that does try to make a girls 12th birthday meangful and attempts to steer all celebrations of this birthday in a way that is likely to increase awareness of what it means to be a bat yisrael.