I've tried to explain why, but because we are not communicating, maybe pictures will help.
This has all of the perspective features you describe but the surface is flat:
Where is the visual curve?
Here is visual curve:
In this second image, perspective is applied just as in the first, but now the surface is convex.
Perspective doesn't cause that appearance of convexity. If the surface isn't convex, then light must bend to produce that visual effect. But straight line light and perspective don't produce the visual effect you say it does. The reasoning isn't sound and it isn't born out in either reality or when modeled.