I wish some national leaders would think more about service to their nations, and less about their own precious egos.
Do the right thing, whether it's good management or looking after those unable to look after themselves, and the rewards will inevitably follow.
But aiming for publicity and image at the expense of actually doing the job, that's bound to fall over sooner or later.
The Duke of Wellington didn't go out of his way to curry favour with his soldiers. In fact, he thought they were a pretty uncouth lot, and said so more than once.
But his soldiers loved him, because he was "the bugger that beats the French", and if there's one thing a soldier loves, it's being on the winning side.
You are right about a leader setting the example for the company. They are the epitome of how to succeed, and others will emulate them. If they serve others, their subordinates will do likewise. If they look out for themselves alone, so too.