Why would 1/d express the force of gravity rather than 1/d^2?

First of all, I would like to congratulate you on asking a good question.

I don't see many of these on this forum.

It can be shown using calculus that the force of attraction between an object and an infinite plane drops off as 1/d. I say infinite plane, because

if the plane had edges, there would be some bizarre effects that would go

on near the edges.

Effectively, for a localized region of the earth in the flat earth model, it

could be considered an infinite plane.

The proof for this is purely mathematical, so its pretty much indesputable.