Partita No 1 in B flat major, BWV 825: Praeludium, allemande, courante, sarabande, menuet, gigue.
That is, Bach thought fit to name all the parts of this composition according to dance rhythms (except for the prelude).
The fact that later composers use tempos (allegro, andante, presto) to name movements does not mean that the dance is gone, simply that the connection is looser.
I'm willing to bet that two hundred years from now, the classical 20th century music people will be listening to and building on will be tangos, waltzes, rhumbas, jitterbugs, salsas, cha chas, and folk songs. It won't be Cage.
Joanna