Why is film dancing often not to the music?

There is probably the practical consideration that the music is piped in afterwards. Irrelevant.

Presumably there is something played, or at least some count going as the characters are dancing. And it is not difficult to dance on the beat of a waltz or English country dance, I promise. Rather the opposite, in fact--it is much harder to dance against the music. (And, really, if you can't waltz effectively, you should probably get your inner ear checked or something, because I'm pretty sure that means you have the creeping crapulence.)

So, assuming that not every British actor in the history of forever is rubbish at music and dancing, some sound editor is totally rubbish at his job. You can speed up and slow down music without appreciably changing what the audience hears; at any rate they are probably more likely to notice people dancing at a totally random tempo than a harpsichord that plays in a slightly different range of tones than normally.

In low budget monstrosities of garbage, I wouldn't mind. So, for instance, the Star Trek episode in which Kirk is waltzing with some young lady ("Requiem for Methuselah," for those of you keeping score at home), I condemn it but am aware that this is absurd. In your bog-standard Austen adaptation, though, if you're going to go to lengths of verisimilitude such that everyone is dirty all the time, you should probably take care not to imply to everyone that no one in 19th century England had any sense of rhythm.