We have lots of them around here.
I haven't noticed any kind of pattern where their roots cause trouble. Other trees and shrubs grow right up next to them.
They're flimsy- when there's a moderate windstorm, the cottonwoods are the first ones to lose some branches.
The wood is light and fragile. I've cut and split some for firewood, and it's not as useless as I expected, but I only did it because the neighbor dragged the trunks over into my yard. I certainly wouldn't have put any work into going elsewhere and acquiring it.
I've read that the buds make a
useful healing salve. I made a batch last year, but haven't tested it against, say, calendula.
Overall, I wouldn't be afraid of them.