Well, we do inhabit a three-dimensional world in which the inverse-square law holds only approximately, and when a more accurate theory was arrived upon, it turned out to be weird and anything but simple.

Interestingly, when the perihelion precession of Mercury turned out be an unsolvable problem for Newton's theory, there were serious proposals to reconsider whether the exponent in Newton's law might perhaps be not exactly two, but some other close number:

As a result of the failures to arrive at a realistic Newtonian explanation for the anomalous precession, some researchers, notably Asaph Hall and [Simon] Newcomb, began to think that perhaps Newtonian theory was at fault, and that perhaps gravity isn't exactly an inverse square law. Hall noted that he could account for Mercury's precession if the law of gravity, instead of falling off as 1/r^2, actually falls of as 1/r^n where the exponent n is 2.00000016.

Of course, in the sort of space that general relativity deals with, our Euclidean intuitive concept of "distance" completely breaks down, and r itself is no longer an automatically clear concept. There are actually several different general-relativistic definitions of "spatial distance" that all make some practical sense and correspond to our intuitive concept in the classical limit, but yield completely different numbers in situations where Euclidean/Newtonian approximations no longer hold.