I use a different definition of natural. The fact that the electrons, negatively charged, were moving wasn't known when they assigned the positive-negative labels. But still, although what you are saying is certainly true in proton/electron systems, it would be completely reversed in antiproton/positron systems, where the charge would be moving together with the particles. Also, don't forget of ions, or particles in space, or in particle physics experiments, where both charges move.

The point is that the natural choice that you assign would be natural just because of some contingent conventions, but it's not more natural in terms of some more fundamental/mathematical meaning. While the pi vs. tau is.