Great question! I think opening presents after ANY party is the more polite thing to do. Like you, I've never understood why children's party built in this painful, and exceedingly boring, process. At one of my baby showers, a friend gave me a great gift bag filled with maxi pads, Tucks medicated pads and lots of other things I'd need after the birth that no one told her about. It was hugely embarrassing to pull all this stuff out of the bag and not understand why I was getting it. To this day it remains the single best baby shower gift I ever received but it really wasn't at the moment.
I solved the gift problem with my children but making sure our parties were either "no gifts, please" events or very low key events where gifts were not the primary focus (the activity was). This seemed to work for me and my family. My children, now teens, associate their birthdays with extra special time with family, not a gift-fest. The only exception was their 13th birthdays when they had their Bar Mitzvahs.
Thanks for your post!