Yes, mosquitoes do pollinate and do feed larger animals.
But there are a lot of species of mosquitoes, even a lot of species that feed on humans. If we wipe out a particular species that feeds on humans, it will probably be replaced by another species that feeds on humans and the animals that eat them will adapt. Pollination is usually more specific.
Reducing annoyance means reducing the total population of mosquitoes that feed on humans, at least locally. That would have a bigger consequence for the species that feed on mosquitoes, though I don't know how big.
I've been wondering about good new topics for LW, and prediction might be one of them.
The effect of the Zika virus-- and human reactions to it-- on birth rates has the combination of being hard enough to be interesting, not being heavily plowed over by partisans, and having a quantitative outcome.
There's a lot of evidence that Zika causes microcephaly, but this isn't confirmed. There's also some reason to think it increases the rate of miscarriages.
Human reactions cover a wide range, including trying to wipe out the mosquitoes, increasing access to birth control, abortions, asking people to put off having children, creating a less-mosquito-friendly environment....
My assumption is that zika will cease to be a serious problem in not too many years, as more women get the disease and acquire immunity before their child-bearing years, but admittedly, this is assuming that zika (or some other disease with a similar infection pattern) is the problem.
Any other good prediction questions?