Two things.

Thing 1: What if all the restaurants served ten course meals with filet mignon as the main. Then everyone would complain that the "food system is broken" because everyone knows that not everyone can afford filet mignon.

Thing 2: The problem with influence is that it's a two edged sword. An athlete (or other entertainer) who is a good sport will suggest good sportsmanship to those who watch him. On the other hand, a thug will suggest thuggery. In like fashion, a president who is reasonable and seeks to serve wisely will suggest a spirit of wholesome cooperation in the people his administration serves. On the other hand, a President who "won't back down," who insists he'll "get this done," even if the people clearly don't want him to, even if what he's so insistent on is unreasonable and destructive will instill unreasonable adherence to untenable and destructive pursuits in "the people."

Influence isn't optional, it's inevitable.