In dance music we have 2-bar (and 2^n) musical phrases (2 bars "belong together", the first is more accentuated than the second.) Often dance figures, especially the basic steps are constructed that way.
So as an instructor when I count "12345678" I counted two bars in 4/4 timing, but I count the first four beats only in my mind and the second four beats for the public. So the couples start on the next "first bar." It is nothing wrong in counting "1234" but it would be better when doing so to take the second bar. Theoretically that method would even be better, because we don't have a 8/4 timing, so there are no beats "5678".
By the way: in 3/4 Waltz timing a start with "78" or so would be completely unacceptable, the coresponding count would be "456". But how to bring a person into motion by counting genarally can be done by many other ways. So the dance teacher could count a long "3---4-and" or what he feels fitting the music, perhaps "schnubbel-dubbel-dooo" ;))