From my own middle-class upbringing:
I seem to remember the odd phone call, but no cards - and certainly no money - from anyone. I mean, my parents did put their hands in their pockets when I upped and went to university, but as for A-Level results, no way.
Why isn't it done here? No idea. But that's like asking why do we drive on the left! We just do.
(There probably is a reason, but meh...lost to the winds of time, or someone remarkably boring with a lot of time on their hands for research...ie, not me!)
It probably is to do with the fact that more is made of the "big" birthdays. In my house, it was the 21st that got the most attention, but that obviously differs from household to household. Plus my family were a bunch of bluff old tradionalists.