Think of it as asking for a blessing rather than permission. You're joining their family.
I wouldn't do it if the woman had a bad relationship with her parents, or if either she or they were liberals of the type that would find the notion offensive.
Most women I know appreciated it, not because they felt that permission was necessary, but because women often love it when men behave in traditionally gentlemanly ways. (Deep down, they want to marry an Austen hero.)