I think that's a bit of a scope creep. The study of dynamical systems is obviously important and is sometimes rolled into chaos theory, but it predates it - and tellingly, it almost never concerns itself with chaotic behavior, because you can't do a whole lot with that.

So it's sort of like saying that the physics of black holes are very useful to us day-to-day because we want to make sure we don't fall into any black holes.

I'm not saying that chaos theory isn't interesting. It's just that it's pretty hard to find any concrete application of it, beyond hand-wavy stuff like "oh, it somehow helped us understand weather".