I think it somewhat depends on how the presents are opened. I have noticed that if you do the 'open presents with ...' so that the whole household is opening at once - then the present pile is depleted right away usually. If the Sims open one at a time - they seem to last forever!
I admit that sometimes I exploit it and sometimes it just feels too cheaty depending on what sort of story I am playing - plus if you leave them out, the Sims are always getting whims to open a present. In the game I am playing now - I even got just the smallest present pile to see if it would do the same as the big present pile and so far it is still going strong through 4 generations!