This sounds like a plausible optimization, but has not probably been implemented for the Mathematica virtual machine yet. An alternative you suggest would ask the compiler to unroll the outer loop automatically, based on the extra information on vector dimensionality. In a way, you found (for this problem) an efficient high-level way to manually unroll the outer loop (the one over the coordinate index). You can see from CompilePrint that this is indeed the case for fun1 vs fun3. Because this is what matters the most - you must have as few instructions in an inner loop as possible.

The fact that you can decompose the problem into solving for sums of individual components is what makes your second function efficient, because you use structural operations like Transpose, and, most importantly, this allows you to squeeze more instructions out of the inner loop. The rest of the inefficiency is, I believe, inherent to this approach.

This function is still slower than yours, but about 3 times faster than fun1, for such small vectors. (by the way, I think that the speed comparison is more fair when compiled to C, since the Mathematica virtual machine does, for example, much more heavily discourage nested loops). Often we need to process data consisting of a list of coordinates: data = ]

Wolfram mathematica function of list