Where I live, the most abundant non-native plants are suburban lawns. If you're taking this fight home, please familiarize yourself with your HOA bylaws (if you have one). You may be surprised at what qualifies as a "garden", and what you must cultivate in terms of a "lawn". There are practical limits, but there are also workarounds.
The second biggest problem I face is that native plants here have a very bad time standing up to invasive species. Namely, kudzu and about three other species of vines and bamboo. Also native tree species like locust are very good at sending new suckers far into open spaces. So letting my greenspace simply go wild is not enough - a planned and perpetually maintained approach is a must. While it's possible to do all this with less effort than mowing a lawn, that's not a guarantee.