Natives cant be invasive - it can be aggressive in its environment. The amount of sun will limit its spread. Its also food for wildlife.

http://www.restoringthelandscape.com/2010/10/native-plant-of-week-staghorn-sumac.html

If it's staghorn sumac, per Old Forester's link, the stems will be distinctively velvety-textured, supposedly like the horns of a stag. Staghorn can have red stems. You can also rule out winged sumac by looking at the stems for a membrane between each leaf. If it doesn't have that then it's not winged. If it has red stems, it could also be poison sumac although the pix on the internet of poison sumac don't have serrated leaves.

From the flowers it also looks like Tree of Heaven although those don't have serrated leaves.

Well, natives can certainly be undesirable too. But this is in a public park, along with a lot of Poison Ivy, too... So, certainly above my paygrade to remove either!

Yep. Think of white-tailed deer and the pine bark beetle. Can't think of any plants right now but I'm sure the people on this forum can think of some.

Looks like smooth sumac (Rhus glabra). Flowers wrong for staghorn and no visible wings.

Rhus glabra