BBMF obviously doesn't have enough funding to acquire a Mosquito. Besides, the Lancaster was a pretty big exception to the "BBMF" mission, but to add another non BofB aircraft to the collection would be stretching a point. Likewise, the general public knows what a Lancaster and Spitfire look like (and a Hurricane to some degree) but a Mosquito? Maybe not.
Personally, I don't know why the whole lot isn't sold off. It's not as if they wouldn't re-appear in civilian hands, and the cost of operating the Flight could be saved. BBMF is a great idea and I agree with its aims, but as the subject of this thread illustrates, you get into a situation where lots of aircraft have a legitimate claim to preservation and operation by the RAF. It would be difficult to argue that a Spitfire is somehow more significant than lots of other aircraft types, so given that the RAF can't operate them all, why operate any at all?