Reminder: Your lawn isn't "being invaded by weeds," it's undergoing natural selection.
Especially ironic when suburbanites rave about how houses are infinitely better than apartments because they're "closer to nature." You want to be closer to nature? Let natural processes work and have a lawn of whatever grows in your area naturally (even an "invasive" species is better than lawn grasses, unironically, and lawn grasses are almost always also non-native species, just ones that can't actually survive in the environment.) Don't water, don't mow, don't fertilize, just let nature do its thing. It will also attract more pollinators, birds, wildlife in general and instead of a lawn, soon you'll have a natural meadow in your yard. That's nature, a lawn that needs excessive water, chemical fertilizers, and poison just to maintain isn't.
A major overlooked ecological value of parasites and the diseases they carry is population control. We all hate them and the off chance of getting a serious disease from them, but they do help keep populations of mammals in control. Also, some mosquitoes are pollinators.
Generally, if the question is "Should we eradicate native species?", my answer would be no regardless of species because ecology is extremely complex and we likely will never exactly understand the impact of voluntary species eradication until after we do it.
There are non-native mosquitoes and ticks though, eradication of those should be okay unless maybe if they've been naturalized for a long time. Less severe population control near urban areas is probably the most reasonable compromise between not disturbing native ecology and human comfort.
we likely will never exactly understand the impact of voluntary species eradication until after we do it.
Then keep a totally self contained population segregated while we find out. Then if we find proof they're absolutely critical for something, reintroduce them. Otherwise, fuck em.