They could, but if their donation ads said for example 'please help us to take more photos of live events' instead of 'we need your help to keep wikipedia alive' then they would not get half the donations they do currently, which is the point.

I agree, that you can lie to people to make more money. That's called fraud.

I wonder how well they would go if you could target your donation. Humble bundle did this and I appreciated it.