I would guess the main cost would be licensing and bandwidth. While they obviously produce a lot of their own content, not everything shown on the BBC is an in house bbc production. We can also consider the impact it would have on a show that would probably get a DVD/blu-ray release.
The point is, even if we consider the BBC is a service, and implementing access to archived content is within easy reach, expecting it all for free, forever, is silly. I think a lot of people would pay up to £5 a month for iplayer as it is, never mind for every single show the bbc has ever made, all one click away.