'Democracy governed directly by the people' is it even possible?

Democracy is not possible on a large scale. There are no judges, no recourse, no law enforcement, no laws really. If 51% of a nation decides to imprison and slaughter 49% of the nation, it is completely fair game under a "democracy" because the majority of people have had their say. Democracy as a form of government does not and cannot exist, especially in the US.

But if we have to label the US with some sort of "ocracy", since our Republic is made up of democratically elected representatives, it's comforting to say "democracy". Not that it's really the case. We are a "Republic of Democratically Elected Representatives", or "Constitutional Republic" as is the shortened version of that.

Maybe a "Constitutionocracy", or "Rule of the Constitution" would best describe the US.

if 'the people' is entire entity and everyone decides on equal basis, doesn't that make all decisions an average solution, not the best one?

Yes! The country would become a "mediocracy".