If a singing act dances, they can't sing (apologies to Gene Kelly, whose Dancing in the Rain was wonderful, but it is doubtful it was one take, and Mr. Kelly always considered himself a dancer). Dancing as a performance must be seen. Singing must be heard. The two arts appeal to two different senses. Dancing is successively enhanced by music. Singing is distracted by dancing. Sure, there is an audience for that sort, but there are audiences for many entertainments that are questionable.
Sometimes, for many people, a lyric fails to be achieved in singing for the want of breath that is needed for walking alone. Singing and marching is an effort. Dancing takes even more breath. Singing and dancing simultaneously by a performer is doubtful. Dancing and moving lips to recorded "singing" is more probable. The singing is immediately secondary, and if it was primary, what is the dancing for?
Singing on records and radio works well. One can enjoy the performance, the singing, away from the invisible singer. There was a story of some great conductor introduced to the phonograph. He was very pleased, he could enjoy the singing without seeing their faces.
Worldwide there has been a tradition of the blind singer, and other musicians. These performers are not impressed over their own appearance, how can one visually approve of what he cannot see. It is not only the blind who sing with eyes closed. Before the electric lamp, with fire and moonlight alone to illuminate the evening, people sang before their circle of companions. They were not performing visual spectacles.
Tune and lyric, and if fortunate, tone and timbre are the essence of song. Words add to the art and depth, but nonsense lyrics suffice for song. It is possible that early song was wordless. Tune and tone and the emotion to propel them are song, certainly music.
Dancing 'singers' may make millions in their shows and have devoted fanatics, but they are not real singers. You see my point. Still, argument (reason) only convinces some, perhaps few. If you had come across this essay, without coming across the earlier essays, and it had been about politics or religion--few people would have made it to the end.