Apart from the fact that it helps you get a better feel on the sticks, I think one of the main reasons why people use a strap is to support it so you don't need to hold it the whole time whilst flying. You could get a bit tired and when you go and flip throttle hold or an idle up you drop the thing.

I've seen it happen, definitely not a pretty sight! It leaves you with about 2 second to pick it up, find your model, re-orientate yourself and correct.
Anyone who doesn't use one, I would like to hear why. It's ok having co-pilots, fail-safes, training gear and whatever else, but it what about protecting the main control system.
James
PS: One disadvantage is for fixed-wing pilots who I have seen keep their Tx's strapped on while they are starting they're engine, and then their 12x6 chops through their 3810 or 9c. Seen that happen too!