I am (not untypically) on both sides of this discussion.
On the one hand, yes-it's all to do with the capering (and a few other less obvious subtleties). The days of being able to caper onto a table are behind most of today's dancers (apparently "back in the day" you were too old for the Cotswold Morris once you turned thirty!) and with the best will in the world the dancers can't hang on in mid air till the band reaches the next carefully timed double-length beat.
On the other hand, sides do tend to rely on the music to enable them to keep together. (Yes, I know we should practise more, but even in Winter there's still all that "hedging and ditching our time away" to fit in.) In our side, we tend to have the wall of sound approach for the full side dances, especially in noisy surroundings, but for one- or two-man jigs always a single instrument.

SJ