Presidents, in contrast to leaders in parliamentary systems, may be more likely to be seen as leaders for all the people of their nation, not just some of them, because
they do not run with the support of a particular political party
they are elected by the people, even if indirectly, not by a political party
they are required to share office with a vice-president who is demographically different than them in a significant way (such as gender, race, regionality, religion, etc.) in order to provide more voters with a leaders likely to share some of their demographic characteristics
they adopt a tone of humility and inclusiveness in their public speeches