Some dances prefer their own proper tunes, especially if they're at all idiosyncratic - "Jenny Pluck Pears" for example - while others aren't so fussy. Though in some cases it's the tune that makes the dance, e.g. "Levi Jackson", you can throw in other tunes as long as you start and finish with the original.

One advantage of a set tune is that it can help dancers recall the moves. This can work both ways though: I was once in a display side which deliberately practised "Newcastle" to all sorts of different tunes, thus disabling the dancers' auto-pilots so they had to THINK (I wouldn't recommend Steeleye Span's "Robbery with Violins" although it almost worked).

BTW there are moves afoot to restore some of Playford's original tunes where substitutes are commonly used. Try "Hit and Miss" to the original rather than "Daphne", and with a straight hey. A few need a bit of musical effort to make them work - UK dancers might encounter them courtesy of the band Playford Liberation Front.