Invasives from Hell
Some probably got where they are because they fit with that old, olde saying that one man's spinach is another man's poison ivy. Don't you suppose? In this part of the world, bindweed was once planted beneath fruit trees - deliberately. . !
If you want a lawn of it, and some men do, plant Achillea millefolium and allow it to go to seed. Since you probably want to enjoy its flowers, like the ones of cultivar Cerise Queen, having it self-seed is likely.
Now, understand that this Achillea is a native. You can probably find it quite easily in the wild. Achillea filipendulina is not a native but this yellow flowered version has, somehow, jumped the fence in a few locales.
From plantings in perennial beds, Achillea can travel. Dad liked the native yarrow "filling in" on the south slope of his lawn, near a large tree. It really wasn't such a horrid plant and not an uncomfortable carpet. I imagine that the new residents have killed it with an herbicide by now. However, it is likely to have been only replaced by bare ground.
What other plants can you think of with their own designs on your landscaping?