I don't mow down or pull out the dandys, In fact I use them, I raise tortoises and it is a big part of their diet so I am happy that I have some. I just make sure that they are picked back quite often, before they go to seed because otherwise they would spread like fire. They are pretty indestructible, i find them under the snow already green in the springtime.
Its funny, where I live people pay a fortune to have perfect lawns, Not me, and I think I get something better in return, i have song birds, I get ducks and I have small creatures i so adore. I know they come back because I do not use herbicides and have a pretty balanced ecosystem. Dandy's are fine they can stay along the driveway.