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.
Eh? Climbing at max rate or max gradient offers no guarantee of terrain clearance. There will be many circumstances in which climbing at 1/2 max rate offers perfectly adequete terrain clearance. There will be others in which Vx won't get you over the obstacles.
The choice of speed is most affected by how much performance excess you
have. In a light high-performance aircraft, frying the engine in a blind Vy climb is simply daft. In a heavily loaded basic type, you may need to keep it close to Vy to get the climb rate you
need.