[elihu]

You've turned the question around. I don't think it's particularly important that people relate to their leaders. However, if leaders can't relate to (i.e. understand) the people they lead, then you might end up with misaligned goals and motivation.

For instance, if the president of the country is wealthy and associates almost exclusively with and identifies as a wealthy person, then that person might consider their primary goal as president to promote economic growth as measured by the stock market. Some less well-off constituents might rather the president focused on programs to improve access to food, health care, and education for the less well-off.

This isn't an either-or thing; a president could do both. However, if non-wealthy voters think the president doesn't understand their situation or have any policies in place to improve it, then to that voter is not likely to have a high opinion of that president.