I am starting to somewhat embrace my 'native weeds' to the point I am actively trying to identify and include them in my plant list. I've allowed buttercups to colonize the foot of a weeping willow, which is a tough spot for anything to grow. I've even weeded the buttercups so they look like an intentional planting. The flowers are quite jolly and the foliage robust. I also occasionally let my burdocks go in a flower bed, they have some architectural interest here and there. I don't let them go to seed, and they are a bit difficult to dig out once they've put on some bulk. Two natives I let colonize at will are western bleeding heart and maianthemum - both fill in voids nicely and are also easily pulled if they get too happy.
I think a thread in the Natives & Wildflowers forum might be an appropriate place to discuss the pros and cons of common weeds, which are usually either true natives or introduced invasives.