It depends on the particular tradition, but in capers in particular the musician needs to adjust to the dancers as much as the dancers follow the music. I'm sure there were exceptions, but in many cases sides danced to a single musician and the trend to larger bands seems to be relatively recent.

In my personal opinion a solo musician is to be preferred. However many modern sides dance so badly it probably doesn't make much difference.

I suspect the schools pack is aimed at involving as many children as possible rather than strict authenticity.