Great topic, Graeme. I generally tilt the bow a bit back towards me so the hair angle parallels the angle of the strings (and allows me to play mainly on the flat part of the hair). I do this for two reasons: (1) I seem to get better, clearer tone and (2) the bow does not slide down the instrument away from the sweet spot.
I can’t think of any type of lick or exercise in which I intentionally play on the side of the bow hair. Unless you are specifically going for kind of a whispy tone, I would recommend sticking with the flat part of the hair and angling the bow slightly back towards yourself.
But that’s just me. Any other fiddlers out there who can speak to how playing on the side of the hair helps them acheive a lick or a specific sound???