Dandelions were brought to the new world by a Greek physician as a medicine (either in the 18th century or in the 1800's, someone can fact check me, i am too lazy). And, they were successful in reseeding much to the dismay of lawn purists. Soon dandelions were everywhere and frequently unwanted. Personally i love dandelions and grew them in a garden in the US Pacific Northwest, on purpose in their own bed. Dandelion roots have a special B vitamin (most potent in the Fall) generally only found in mammals. Being a vegetarian, this was of interest to me. In addition to what
@Beth_B said about their appeal to bees, the roots can be roasted and brewed like coffee, and is delicious. The young leaves are tasty in salads, and i think it is the flower that dandelion wine comes from (need fact check). They are also cheery little flowers. So, congratulations on your lovely dandelion crop Beth_B and your enjoyment of having them

Personally, i think your lawn is lush and lovely.