I have lived with mimosa for many years without any signs of invasiveness from Alabama to Oklahoma. I daily roam quite far afield examining flora, fauna, and water creatures always keeping an eye for useful or invasive species.
There is currently 3 mimosa within sight of my house that have shown no signs of invasiveness. The largest is about 15 years old, I tried to collect seed from the plant but close examination shows 95% damage due to a tiny larvae that bores into the pods. The rest don't sprout, I couldn't even get any to germinate in paper towels. I am trying to study the larvae with amateur equipment, I'm afraid.
So I dug up a rare small volunteer and planted it in my yard alongside a native mulberry with the constraint that the first one to five feet could remain. I had to cut the mimosa. I just needed something to cover my propane tank and the size and habit of mimosa makes it the preferred plant, constraints aside,
It's my grandmother's fault, way back in Daviston, Alabama who had one when I was a boy. I'm still looking for another one.
One thing I don't see in the comments is about the roots. My neighbor has a mimosa that grows close to the fence dividing us. I can't plant anything on my side of the fence close because the roots of the mimosa are so invasive they choke out my plants. If I dig, I find a mass of hair-like roots crowding out my plants. Personally this the killer for me. I have a great dislike for this tree.