The Relationship Between Electable and Governing Well

It's hard for me to think of a setting which this problem wouldn't apply at all. A good example is actually the ancient Chinese imperial examination system. So I could imagine how a mastery or even a deep appreciation of that could theoretically apply across a number of skills. Theoretically, yes. But we don't have historical data to prove that being the best at classical poetry means you're not the best at tax collection.