Dandelions are considered weeds in a botanical sense because they are non-native invasive plants in the United States. Same with clovers, crabgrasses, dallisgrass, and many other common lawn plants.
That's only true for certain species in the Taraxacum genus. There are many Taraxacum and other chicories native to North America which most people would still call "dandelion".
Most popular lawn grasses were created using selective breeding. People will argue about whether they are properly considered native to anywhere, or whether they belong in some third category of man-made organisms.