Your honour, the case for the defence:
They're quite different people and Adam has always been the showman, the communicator. Initially, Joe probably had to steal himself to do all the press for his film and if he hadn't been able to talk confidently about something he knew so thoroughly and passionately, I think we'd have seen a lot less of him. I can't imagine him doing stand-up like Adam but never say never! He doesn't communicate - I presume you mean via social media - because he's worried he'll make a plonker of himself and can't handle the ensuing self-loathing. Adam is quite happy to make a tit of himself (possibly because he knows how endearing it is) but he has a great comfort with honesty, however daft it makes him appear, which Joe is more reserved about, especially when he's on his own. When they're together and one does something silly, the other one pops them back up and they're back on balance.
I think you might underestimate the amount of preparation they put into the radio shows. They may sound random and shambolic but both of them prep for that. Adam, of course, spends many, many hours making his jingle jongles. Some of the most beloved episodes and snippets from the shows would not have existed if time had not been spent making them happen. Adam thinks hard about the minutiae of life and does songs and jingles; Joe brings soundbytes like The Archers, Wonders of the Universe, Blah Boopity Baya etc. It's the blend of the prepared and the spontaneous that we adore and I think the balance is often misunderstood.
Furthermore, I don't think either of them feel as comfy doing the show without audience interaction and that may be why they didn't feel like doing the Christmas show. In 2010 they tried to get some pre-action via the blog and Twitter but it's not the same as having people text & email while they are in the studio. Joe has often mentioned this. I also think he's very conscious of the vagaries of the film industry and must feel the need to keep irons in fires. However, I suspect he might not handle multi-tasking as well as Adam.

If he worries about turning up with the show each week, he can't knuckle down and do the research & writing he needs to do. This is all conjecture, of course.
This couldn't go on forever. Nothing ever can. Adam was asked the question down in Sydney last night and implied that they were both too busy this year. Adam is more and more in demand and I really do think we're not far away from a serious TV commitment from him. Once again, this is purely conjecture.
You may argue that Jonathan Ross, for instance, can manage to do a vast number of diverse things but he's a different person and he has reached a level where he has people to help him....a lot.