So, those who want to parent (rule, guide and lead... goveren) children are inherently different beings than those who want to lead, guide, and govern parts of society?

But they are not so different.  They, leaders and governors, are often parents themselves.

Wanting, or being willing, to governmen children or otherwise is in fact not ipso facto proof or even evidence that the willing are least suited to it.

In fact if they were so unsuited to it, the example of their parenting would reflect it and we would indeed have no society left.  But, as most governors are parents, the locus of the flaw is not merely shown in the desire to govern.

Further we can skew our description of parenting to show the incentives are similar.  We are wired to raise our children (in part) precisely so they can serve us later on in our older years.

I'm not saying the state or our system is good.  This rationale for the major cause of the problem just doesn't pass logical muster as regards human nature.

You're observation of incentives has more explanatory power than a blanket view of the nature of humans.