
Tree-of-Heaven is on the hazard list here, which shifts the odds toward removal. It is illegal to sell, gift, transport or plant in Indiana under the state's Terrestrial Plant Rule, and it is the preferred host of spotted lanternfly, now reported across roughly 17 Indiana counties. Between the legal status, the brittle wood and the suckering, this is the one tree on this list where the professional answer is nearly always removal rather than management.
It rarely declines gradually; the notable exception is Verticillium wilt caused by V. nonalfalfae, which produces wilting, yellow vascular staining and dieback and can kill a tree within a single growing season. A tree-of-heaven suddenly wilting and defoliating in midsummer is far more likely wilt-killed than drought-stressed, and the standing dead stem turns brittle and unsafe to climb very quickly.
Brittle, weak, coarse-grained wood that fails under loads native hardwoods shrug off, which is why it is treated as a removal-first species. Its fast growth builds large diameter without matching wood strength, so a 40 ft tree-of-heaven over a roof is a bigger storm liability than a 60 ft oak in the same position.