I think you'd have to define beneficial..... Any species with sufficient biomass will become part of the surrounding ecology, with several other species adapting over time to predate upon that biomass.

Both tics and mosquitoes are huge sources of food for animals like birds, bats, fish, amphibians, and especially other insects. Completely destroying them would likely lead to an ecological disaster, just as it does when humans attempt to sanitize any aspect of nature.

The sanitizing process of urbanization is one of the largest reasons mosquito populations have exploded in North America in the last hundred years in the first place. Instead of mosquitoes laying eggs in ponds and waterways that are filled with frogs and fish that normally control their population. They are laying their eggs in urban environments that the animals who normally govern their population cannot thrive.

We don't understand the intricacies of any ecosystem nearly enough to start engineering it. Pull one thread, and you might unravel the tapestry.