I' ve never understood the convention that road bike "standard" was 170 but mtb was 175. the standard explanation is that the longer cranks give more leverage for climbs, as if dropping a gear wasn't an easier option.
That's part of it. Convention is that shorter cranks make it easier to spin which is what you do on a road/track bike. Longer cranks give more leverage hence why they became standard on MTBs.
Of course all this was back in the day when you had 5 or 6 gears (7 if you were minted), nowadays road bikes can have 33 if you have 11sp Campag with a gay triple, MTBs are at the 30sp stage (just) so it's less of an issue.
Shorter cranks help for DH cos they give fractionally more ground clearance, on track bikes 165mm is normal, partly for the spinning reason, partly for clearance (clouting a pedal as you go up the banking is not fun!)
175mm for all my bikes except the track bike and the roadie SS where I have 170mm.