I do not think the exact shape has any influence, especially potentiometer or audio jack placement.

It influences playability, which is functionality. Fender's marketing advertised the shape as a functional feature: body carve for easier playing standing up, double cut for easier access to higher frets

> I do not think the exact shape has any influence

Yes, that's what I said.

Haha I was going to say that but I thought, no, I don't need the downvotes. Lots of guitarists here (including me)