If the female is shooed away before it gets a full tank, subsequent hosts could get something more out of the bite. (Be careful of the company you keep, IMHO.)
The problem is one of politics and attribution. First, it would be difficult to prove the mosquito was the vector, especially when so many 'more popular' vectors are available.
Second the PC rainbow nazis could never allow such a thought to get out. No one would want to be anywhere near the most likely carrier groups during bug season, and there would likely be enough public outcry for removing them from parks, etc.
It might hurt their little agenda.
I think the problem with the mosquitos theory is that mosquitos don't transfer enough virus to the host.