I'm all for eradicating the diseases, but not really a fan of wiping out entire mosquito species. Eliminating biting mosquitos may have a knock-on effect... possible unforeseen effects that may adversely affect entire ecosystems.
There may be certain species that have evolved to hunt/feed on specific mosquitos, and in turn, other species that rely on these. When they are displaced because of this, it's possible that the checks and constraints on certain species will be reduced.
They may not be efficient pollinators per insect, but they may yet pollinate certain types of plants in certain locations that no other species do efficiently due to sheer numbers.
Of the 3500 species of mosquito, only 6% bite humans. Of the 200 indigenous species of mosquitos in the US, only 12 of them bite humans. Mosquitos are the world's deadliest animal, killing a million people a year. Moths don't kill anyone, and if they're more efficient than bees at pollination, then they're likely more efficient than mosquitos. If we eliminated only the biting species of mosquito, any detrimental effects on pollination or the food chain would be negligible.