No way. I feel like asking that implies she is her fathers possession. I find the idea loathsome.
I'll agree that the phrasing "ask for his permission" makes it feel like an exchange of goods when, in my case, it was more of me asking that he be happy about the prospect of us getting married. If the father in law sees his daughter as something to "own" then he's not worth speaking to period. If the groom to be feels his wife to be is property to be acquired then I feel for that poor woman. -she ought to run. Speaking to the father in law prior to you getting married is not a bad idea though, if all involved are rational and compassionate people. As a father myself, I would take great comfort in a young man asking for my "blessing" and letting me know what his intentions were in regards to how to plan and provide for his family. Could be that I have advice worth hearing. Could be a great way to get a father/son relationship started.
The tradition is clearly rooted in a time when women weren't allowed to decide things like who they should marry for themselves. It's just a bit of quaint old sexism. I can see your point but I really think the practice is rooted in some less than proud old traditions.