No, you're not wasting your time.
I find that dandelions are the easiest to get rid of, and the more you weed them, the less and less of them come back.
I don't use herbicides, so I personally use a sod knife and yank them out. Sometimes a piece of the root may remain, but it doesn't necessarily mean that it will come back.
So long as you water your lawn well (every other day) and apply some fertilizer twice per summer, the the healthy grass will take over.
I used to have a lot of dandelions, now I barely have any. I might get one or two per month, and that's it.