I know you can eat them -- the flowers are okay but the leaves are not good at all. And if they'd take over my lawn I'd be very happy; I wouldn't have to mow and it's pretty in the spring and they are evergreen here. And I know they are of moderate herbal use but I have better options.
But as a weed they are pugnacious and tenacious. I spend a lot of time digging out violet tubers and seed capsules (and putting them in my lawn!). Some are inches long and if you miss a tiny bit, the plant is going to come back. Is there some other use for violets that I don't know about that I can come to appreciate and a use for them I can leverage instead of only viewing them as a weed?