The original idea was that by having a separate funding path, the BBC was at less risk of government control.
The funding is equally shouldered across the population, so the content should be created with equal consideration too. In practice doesn't always go that way, but that was the principle.
It is not about teams being represented the same amount, but about individuals.
Those appointed from outside the BBC tend not to have any background in NGO or non-profits. Bit strange for a not for profit public broadcaster.
It's a very hairy arrangement and I don't think most of the public are aware of it.