A thing I heard somewhere, I think on an episode of the Permaculture Podcast [1], was to stop thinking of it as "invasive" plants. Plants aren't "invading", they're filling a niche that is under-served. The way to keep those plants from growing is to supplant them with other (potentially native) plants filling the same niche, or modify the environment to fix whatever deficiencies the unwanted plant is gaining it's advantage from.
They also tied it into the immigration debate, which I thought was interesting. They mainly played off the fact that the same people who are pro-immigration are often pro-native plants. Is it really the best idea to eradicate species from regions, when we could just learn how to live together more effectively?
I feel like I probably did a very poor job reiterating all of that. We've really enjoyed listening to that podcast though.