The concept behind /programmes is a very strong one: One page for every programme. It doesn't matter what medium the programme is on. It doesn't matter whether the programme was broadcast decades ago, or is due to be shown next Tuesday. It doesn't matter who holds the right to the programme. Every programme gets its own page.
The current problems arise when you start to duplicate content. Recent programmes get added to iPlayer. Some older programmes get added to the archive. Children's programmes get added to the cbeebies site. Flagship programmes get given their own bespoke pages separate from /programmes The solution? Get rid of all the duplicates. Just have one page per programme. If you have the rights to show the programme, embed it on that page. If its a children's programme, add some bright colours and rounded corners so that parents feel its safe. If you want a top level directory for a programme, make it redirect to its programme page. But whatever you do, you need a consistent structure for providing information about the BBC's output across all media.
2. News, Sport, Weather/Shipping Forecast and Blogs. I agree with you that news should be a pillar of BBC Online. (And I noticed you didn't mention blogs on your diagram, so I've stuck them in here).
3. Learning Its important that the BBC help support learning for both children and adults through things like bitesize and Jam (R.I.P.)
4. Knowledge BBC Programmes contain lots of information and its very helpful to be able to reference this information online. Resources such as Wildlife Finder, Recipies and /music are invaluable. It would be great to see resources such as these available in other areas too.
5. Games The BBC already makes games such as Doctor Who: the adventure games and Bamzooki Zookkit. In the press, games are often portrayed as an anti-social waste of time; but they are, in fact, an excellent way to educate, inform and entertain all at the same time. The BBC should make more games.