Steve, it's not so much that "dandelions can stay". It's more that you can't get rid of the buggers once they're in!
At our last house, I reseeded the lawn. It was heavily-compacted clay so I did the job properly, digging in plenty of sand and compost to improve it (especially the top tilth). Because the "lawn" previously had mostly comprised dandelions and moss, the digging-over also involved extracting all the bits of moss and dandelion roots. You really would not *believe* how much dandelion came out of that lawn! It was one beautiful lawn when it grew, so all that work did achieve something, thank goodness.