I hear one school of thought saying you should climb at Vy to pattern altitude,
Exactly. The clue here is in the word 'profile' If you move away from the figures given in the POH, unless you're leaving a completely flat field, how can you make sure that you have adequate terrain clearance. Also, by climbing at teh best rate, in the event of an engine failure, you've got the greatest possible glide range. It's a good idea to occasionally practice Vx, too, for those situations where you have significant obstructions. Another good reason for using Vy if you're flying circuits is to get yourself time on crosswind to properly trimmed for the circuit cruise, so that you minimise height changes while you're distracted doing your pre-landing checks etc.
Cheers,
TheOddOne