These things are apart of nature, and have a fascinating lifecycle - sure they make a lot of noise and wreak havoc with our own lives for a while, but it is wrong to insulate ourselves too much from the natural world.
Regarding mowing the lawn, I imagine chewed-up cicada trimmings make good fertiliser. If you wait a few days till they dry up or get eaten by natural scavengers, you won't get spattered.
Having said all that, about 12 years ago in South Wales we went to a beach near Bridge End, and the whole place was swarming with Lady Bugs - literally millions of them crunching underfoot, getting in your hair and ears and eyes and mouth - it was totally freaky. There is something primeval about not wanting insects too close...