Yes, it seems a really silly thing to me!
Someone once explained to me that the licence used to be only paper at one time - no laminated card, and it seems they just added the ID card to the paper bit at some point. And I think other countries have sort of moved with the times & seem to manage without a paper bit - especially in the age of technology...but then going by how UK governmental authorities seem to (mis)manage databases & technology (thinking of the latest shambles/scandal with UKBA), maybe it's best to keep the paper bit after all.
Not strictly true. I had a paper licence when I passed my test in 1979, I last moved house in 1991 and got a new licence then and it was still just paper. I've only just exchanged it for a photo licence because I was finding I needed photo id more and more and didn't want to be carrying my passport around. It wasn't a case of just adding a photo licence to the paper licence because the paper part of the photo licence is different to that on a paper licence, and you get a different bit of paper.
I think it's because the technology at the time meant that all the information couldn't be held or easily read off the card, for example any disciplinary points so that is kept on the paper.
I agree it's ridiculous though to still need to have the bit of paper.
Incidentally, as recently as 18 months ago I used my paper licence with no problems to rent a car in the US.