"So you assume, then, that “intelligence” (leaving aside the problem of how you might measure it) is distributed unevenly throughout the population. "
No, I don't. Most measures of intelligence result in a bell curve distribution. This means that most people are of average intelligence. But people of average intelligence don't usually end up running companies, making significant developments and discoveries, etc. So (and I know that IQ can be measured in different ways, but I'm using it as a convenience here) if you accept that brighter people have an IQ of (say) 115 and above, then the majority of people will fall into the "not so bright" category.
I don't know of any successful businesses where the shareholders get a significant say in the minutiae of running of the business, and I don't see why a a country should be any different in that respect.