Carrot stretches are the only (well, okay maybe I cheat on my own rules sometimes) way Junior gets fed treats by hand. When I first acquired him, he was extremely impolite and would not keep his mouth out of my personal space. Remember this video? He's a LOT better now after a long period without ANY treats by hand. Showmanship training was also helpful in teaching him to keep his nose to himself. But even though he's better about his manners, I still only give him treats as incentive to do his stretching, or I'll toss one in his feed tub or if he's been particularly wonderful he'll get a treat by hand, but only if he obeys a verbal "Back up!" and steps back from me rather than mauling me.
Stretching is good for him as he, like most horses I suppose, tends to be stiff and resistant to bending.
It's also amusing for anyone watching, and you know how he likes to be the center of attention!