If you don’t give a shit what the answer is, then you aren’t really asking. Your analogy to going to the store doesn’t fly because it’s already being decided up front in these cases that the answers are irrelevant. It’s a pretense of showing respect without any sincerity behind it.
And it’s historically rooted in brokering women as property, no matter how much we try to soften the terminology now. You might as well offer the dad a goat, in my opinion.
What if his daughter is a feminist?
You’re about to be his son-in-law, of course you care what he thinks. That doesn’t mean it’s up to him, but a clear signal that you value his opinion about a matter so close to both of your hearts will be greatly appreciated by some.
It’s a symbol, a gesture, a ritual: it’s not *supposed *to be taken literally.
It proves the point that this ritual is sometimes expected of men and never expected of women. The ritual is pretty benign in it’s modern incarnation, so whether or not “sexist” fits is a matter of how you want to use that word. Regardless, it’s seldom harmful.
If I thought she’d mind, I wouldn’t ask.
But if his answer doesn’t matter then you don’t care about his opinion. You can’t have it both ways. Either his answer means something or it doesn’t. If it doesn’t, there’s no reason to ask. If it does, then it’s sexist.
In the first place, his opinion matters. He doesn’t get to decide for you, but as your father in law his opinion of you and your marriage is going to affect your life. If he’s skeptical about the marriage, then this is a good practical opportunity to talk to him about his concerns and, hopefully, allay his fears. In between “He gets to decide whether I marry” and “his opinion doesn’t matter at all” is a vast gulf, containing most of the real world.
But, second, that’s all extraneous in light of the fact that you ask because you think it will make him happy. Making others happy is a perfectly good justification for most actions, including this one.
I don’t think he is, but it’s worth noting that the OP said “blessing,” other people talked about “permission,” and some of us (me, anyway) used the terms interchangeably.
A good point. I do wonder- were you being hyperbolic when you said she might see you as the woman who stole her son?
Yes, I think it’s a distinction without a difference. Unless the fiancee-to-be is too young to marry without parental permission, you don’t need permission, so why ask for it. And if it’s just a blessing you want, then both prospective partners should seek a blessing from all the prospective parents-in-law – not just the man from his prospective father-in-law.
(Incidentally, back in the dark ages, when I was the prospective son-in-law, I didn’t have to face the issue, since my wife’s father died before she was born, and her mother had never re-married. But I suspect that I would not have asked, even if he’d expected it.)
Only in the sense that it’s a common phrase and a fear of (I think) many young women when getting married. He’s definitely her “baby”, in the sense of being her youngest *and *she’s told me repeatedly that he was the one of her three kids that she always felt closest to. Our relationship is pretty stereotypical: she thinks I should call her more often and treat her as a mother, I think she means well but is overcontrolling and prone to melodrama. She’s pretty much the m-i-l on Everybody Loves Raymond. (In fact, one of the writers on that show is one of her neighbor’s kids and grew up with my husband. I have my suspicions that the resemblance might be more than coincidental.)
My father-in-law was perfectly clear from the start that if his son didn’t marry me, he was an idiot. It was the mom I had to seek the blessing of. I do agree that the “blessing” should be sought of both sets of parents, for what it’s worth. I think that it’s just generally a little less formal and a lot more complicated and subtle for the bride.
…and later…
There you go. Tell him you want him to give you a goat in exchange for your blessing. 
A goat?
Surely the love of your life is worth two pigs and a milk cow!
Done! <spits on hand>