I would suspect that nobody would think as you propose. It’s obvious to anyone that the choice is arbitrary and not in any way “natural”. The number of protons in a nucleus, on the other hand, is in no way arbitrary and describes a number of atoms that all behave in almost identical ways (small exceptions of mass and, for a few, stability). Perhaps you might want to claim that “natural” vs. “conventional” is a sliding scale, with driving direction at one extreme and elements at the other. And perhaps the boundary is fuzzy. For example, the geologic eras and periods were mostly defined originally to be carved up at times of maximal taxic turnover. As such, they’re somewhere in between natural and conventional.
I think you are now getting into a completely different sense of “natural”, which does not advance your point.
Conventional? Is there no such thing as 5 apples, a different thing from 4 apples, other than by convention? I’d say that the natural numbers are abstracted from real phenomena. There is no alternative way to count apples.