Stomping is a waste of time and who wants bug guts all over your shoes? They will wreck havoc for a couple of years and then calm down whether you stomp them or not.
There’s so many invasive plants, insects, and diseases that it’s not worth fighting it anymore. It’s a global habitat now because of humans. All of the continents would come back together in another 250M years anyway.
One good thing about them is they love the invasive Tree of Heaven. So they can wipe that out while other animals learn to eat the lantern flies.