My complaints aren't limited to those in the article.
Lawns with lots of dandelions are usually infected with several other varieties of undesirable weeds, that have no flowers that are beneficial to bees.
Dandelion and other weed seeds often seed neighboring properties that may not want those weeds, and can result in more use of chemical herbicides.
When those overgrown 'terraces' are finally cut much of the grass and weeds wind up in the street where the storm drains carry them to nearby waterways exacerbating aquatic weed and algae growth.
Finally, allowing grass and weeds to grow above "lawn" height 'scalps' the lawn of the tender grass leaving coarse stems that take weeks to recover.
I sprayed the property I manage last fall with Weed-B-Gone (having put it off for too long). This year I have the best looking lawn in the neighborhood. The grass is thick and lush with only a few dandelions poking up. I pick off the blossoms as they appear. However my next door neighbor has chosen to not mow his lawn, which is now full of dandelions going to seed. I will likely have to spray again next fall as his unkempt lawn will likely seed mine. Even as I write this the wind outside is blowing 20-25 mph, blowing seeds all over the place.
No Mow May is definitely not a good idea, IMO.