I haven't been in that situation in my life yet, but here's how I think I would handle it (hypothetically, or course). It seems to me that there's a fine line to walk between being traditional and being misogynistic. Asking permission may be a bit of the latter, even if it is a formality. In some way, it feels like two boys deciding the fate of a helpless girl, and I don't think I'm OK with that. However, informing her father of your intent and asking for his assent seems reasonable to me. I think that way, you can respect the tradition, while at the same time not acting like there's any power sharing arrangement between men. She is a person who gets to make up her own mind, and her opinion is the one that matters.

Respecting traditions can sometimes be seen in very negative ways, given the history of the dispossessed. For example, go down south and ask the nearest back guy what he thinks of the red neck who is respecting the tradition of flying the Rebel colors on his truck. It's an extreme analogy, to be sure, but certainly women have had a long history of possession by men, as well.

All that said, I still think there is value in having a man-to-man with a woman's father, perhaps if nothing else than to let him know that you love his daughter, and you will treat her with respect, humanity and dignity and everything else that she deserves. It's a fine line.