I don't think a bird could be more cuddly than my SC2.
Even when eating, in the middle of playing or talking, my too will stop immediately for any head scratches. He's gone up to an hour of just standing still and adjusting his head/neck for scritches, and if I stop, he'll make little squeaks, nudge and gently beak my fingers until I start again! Or until he gives up.
He's also very comfortable with anyone touching his anywhere - though I don't reccommend it, he will lift his wings to be pet, and I can pet his feet, legs, belly, back, wing muscle and feathers and he'll gladly soak it all in!