Alistair Anderson and David Oliver had an explanation which was an extension of the one put forward by Guest BeauDangles.

Dances often had their own tune and the musicians would play it through as often as was necessary to complete the dance. Even if a dance could be danced to a wide variety of tunes (waltzes, polkas etc.), it was likely that at any time only one tune would be used for the duration of the dance. It was recording that changed that.

You can get two or three standard 32 bar dance tunes on to one side of a 78 rpm record each played twice through. Record buyers wanted variety (and still do) so this format meant that a listener would hear each tune enough to pick up on it, but not often enough that they would get fed up of it. That way sales increased.

If someone was using recordings for a dance club or such, then the dancers would get used to the idea of there being two or more tunes for a dance and dance bands would pick up on the idea and use it. As has been said earlier, this would provide a way of increasing interest for the musicians, though, in the past, they had ways of dealing with the tedium of playing the same tune through many times, in particular by use of decoration of variation.

I'm sure this isn't the only explanation and other factors would have been at play. After all, if there were two tunes suitable for a particular dance it's easy enough to respond the question "which one?" with the answer "Let's play both." I do think there may be a grain of truth in it, though.