From my prospective asking the Father/mother/family's for their blessing is a sign of respect and thats because of the close relationship I have with them. If I wasn't close to them I wouldn't care. I think father's (in paritcular) like to be asked as its the same rite of passage they went through.
Just out of interest, what happens if the Dad says no? Is the boyfriend then not supposed to propose? Or, what happens if the Dad says yes, but the the girl says no to the proposal?
In some cultures the father/family's say is the be all and end all, but I'd imagine most people would respond however they liked (despite what the Dad's answer is).