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Fucking calm down. Most people do it out a general respect for the family of the bride that has nothing to do with sexism. The idea that it's the father that is asked is just a hangover of tradition. The tradition of consulting the family is a good one in my opinion. To assume that everyone who "pays lip service to it" is an obnoxious sexist is ridiculous and egocentric.

I am perfectly calm.
It's not 'consulting the family' it is consulting the *bride's *family. You mean you really can't see the sexism and misogyny in it? You don't get that it comes from the idea that marriage was the transfer of property from one man to another? Asking the bride's parents may ameliorate this slightly but the fundamental is the same; the bride is the passive partner. You must be able to see how crass and unpleasant that is.
And what, by the way, would you do if the bride's father or mother said no?