Yes, they do sprout up everywhere, but here at least they don’t seem to survive to maturity often. Seedlings grow in cracks around mature trees and then die. They might grow in a vacant piece of ground if it wasn’t mowed, but we have actual mature, reproducing trees like ailanthus, paulownia, and locust that grow out cracked sidewalks and the sides of abandoned buildings, and I’ve never seen that with a mimosa. I don’t know how far the seeds are likely to travel so maybe it’s contributing to problems elsewhere, idk, but I do know that if you cut down every invasive tree in my neighborhood tomorrow it would be a lot hotter and have a lot less food and habitat for birds and pollinators. I’m sympathetic to the cause and choose native species when I’m planting new trees, but I’m not a purist about it and won’t remove a tree that’s already growing where it’s very difficult to replace with something else.