It probably depends on the culture, but I think it's old fashioned. Maybe it's because I don't understand why someone would have to ask for permission. That being said, if I ever think about getting married there is a chance I'd still ask for her father's permission haha.
It's so sad that "well mannered" is associated with "old fashioned".
I think it's very appropriate for a guy to ask the parents for permission. Even if they say no and he is still going to go ahead with it, I think it's an important show of respect. It also may give the new husband/wife some security and confidence knowing they have the parents blessing.
I think it's sweet a should never be "old fashioned"