Of course, by rejecting the whole "lady/gentleman" view of "woman/man" as a sexist construct that's well past its Use By date, I'm likely missing some subtlety of lady-like and gentlemanly conduct that the cabeceo protects or privileges. I believe that the two dancers are exactly equal partners, that the leader isn't mostly "responsible" for the tanda, that a follower invitation thus isn't an imposition of responsibility, and that in fact leader/follower doesn't have to mean man/woman. So, to me it's all a bit quaint that we have this ritual of Mr. Dashing Prince inviting Ms. Shy Flower and taking charge of her, and this dislike of Ms. Flower being bold and asking Mr. Prince because it somehow imposes something on Mr. Prince that his invitation doesn't impose on Ms. Flower (hah!).
So, my proposed explanation might rub you the wrong way.