I have watched this in action. The Quaker Meeting I attended in Cincinnati sat on five acres. The back half of it was a little remnant woods. When I first starting attending there in 1971, the woods was beautiful - a complete canopy that included a number of massive old beech trees as well as buckeye, oak, maple, hackberry, catalpa and the forest floor full of native woodland wildflowers. Some how we thought if we just left it alone it would be ok. We fenced it in, put a path around the outer edge and didn't let anyone walk in it except on the path. But it had already started being attacked by a bunch of invasives - Japanese honeysuckle shrub, english ivy, eunoymous, vinca.
By the 2000's it was obvious the woods was dying. We had lost a number of the huge old trees in various storms. That is natural, but they weren't being replaced, because the honeysuckle crowded out / shaded out the tree seedlings, so no new trees were coming along. The wildflowers were mostly smothered by all the ivy and vinca. Since there were now a lot of holes in the canopy, sun loving weeds were popping up. And since there was open space and sun all around the outside, the trees on the outer edge tended to all lean out in the sun. We had to take down a number of them when neighbors complained about trees leaning over into their yards, threatening their houses.
At that point we started trying to save the woods -- cutting down honeysuckle shrub, cutting all the vines off trees, where trees were being smothered, planting new native trees, etc. It is a ton of work, that has to be constantly redone. The first native trees we planted were all eaten by the deer that live back there, so we learned to plant them in cages. When we made clearings for them some of the wildflowers came back on their own and we we planted some as well. I don't live there any more, but even with all the best work we can do, it is clear that patch of remnant forest will never be what it used to be. It is really difficult for an isolated bit of forest to survive in the midst of a city full of exotic invasives.