Wolf spiders will take over. I don't think many people will be happy that they've traded small web slinging spiders for 2" diameter hairy ground spiders.
Wolf spiders do not hunt mosquitoes. The smaller ones may hunt flies, roaches and other terrestrial insects. Weavers will feast on all flying insects, but mosquitoes who are too small.
I know, so getting rid of mosquitoes would get rid of their spider predators, letting would spiders take over.