To add to what aszantu said: plants with deep roots can be very healthy for a garden because they essentially draw nutrients that have soaked deeper into the soil back up. So one way of looking at them is that they are basically mining soil nutrients from below for your garden for free. Perhaps that will make repeatedly mulching them a less frustrating task.

Also, while there are of course legitimate reasons to consider certain plants weeds (e.g. they maybe be poisonous, toxic, or displace other plants that you like more), dandelions are mainly the victim of marketing from pesticide manufacturers half a century ago.