Believe it or not but the american system isn’t exact a blueprint for actual democracy. Many democratic systems don‘t make the election of the president a vote.

In actual democracy, like ancient Athens, most offices are filled by sortition rather than election.

Election is characteristic of oligarchy, where a few people make decisions for the many. Usually the few are supposed to be more qualified for or deserving of office, and election is a way of deciding which volunteer is most worthy.

In democracies, everyone is assumed to be equally qualified, as governing requires no special knowledge beyond some basic morality. So, lists of volunteers for office are compiled and names drawn from those lists at random, and for every office something like nine names are drawn, so volunteers can split their time between public service and their private affairs. This random selection also prevents the creation of political parties: you can’t get randomly selected by spending more on a campaign.

So, election of officers is oligarchic, rather than democratic. Democracies have votes instead on legislation, declarations of war snd peace, and jury trials.

Well funnily enough, virtually all the constituent countries of the EU do put the election of their president to a democratic vote.