You are having fun resurrecting a bunch of old threads, PreserveFlowers!
This was an interesting one. Clearly non-native can be helpful - much of what is in our veggie gardens is non-native.
However, this is somewhat a sore spot for me right now, as I am just back from spending a week volunteering with 20 Sierra Club folks working to remove invasive foreign species in the forest at Mammoth Cave National Park. We pulled close to 500 large garbage bags stuffed full of garlic mustard, but all we did was a small area around the visitor center, entrance to the caves, and beginning of a main trail. We didn't touch the rest of the 54,000 acres of the park.
The garlic mustard stays green much more of the year than the native wildflowers and it grows really thickly and chokes/shades them out. Where the garlic mustard grows, pretty soon no more wildflowers. The garlic mustard is actually edible (it was brought to this country a long time ago as a pot herb). But if you mean your name PreserveFlowers, you shouldn't be too excited about having all the wildflowers wiped out of all our forests, in favor of a rather ugly pot herb. Humans can eat it, but I don't think any of our native birds and insects do.
I do believe what I said above, that we have already lost this war and our beautiful forests are doomed. I did a service trip last year in the Tahoe area, California. They are battling to save their spruce trees from some imported orange fungal disease that I don't remember the name of. And there are pine borers and gypsy moths. Here at Mammoth Caves, besides all the invasive species (we also spent a day cutting privet hedge), the dogwoods are being wiped out by anthracnose fungus, the hemlocks have an insect killing them, the ash trees are being wiped out by the emerald ash borer, the fresh water mussels in the river are being wiped out by a little Asian clam that multiplies in the billions....
If you like forests, go walk in them now and take lots of pictures. In 10-15 years there won't be much left. I try to console myself that eventually nature will come to some kind of new balance. It will look a lot different than the old one, but it won't be forests composed solely of garlic mustard, English ivy, privet and honeysuckle. But that's a process that takes many thousands, if not millions of years, so it is some what cold comfort.