> The very essence of democracy is that he gets to set policy
The President is supposed to execute the laws faithfully. It's Congress' job to set policy. Not that it matters because we hav the Republican Party setting policy instead.
Congress has turned away from that responsibility by giving ever more discretion to the executive branch throughout the history of the nation. Prior to that, "federal agencies" like the EPA, FCC, FTC, SEC, etc., were illegal. All of these agencies are formed from powers that Congress relinquished to the executive branch, to unburden themselves from the difficult job of passing laws.
The Roman Empire had a similar demise as emperors relinquished power to nobles who also didn't want the responsibility.
Government is work and no one wants to do it. Anyone agreeing to take on the responsibility that Congress didn't want has a reason for doing it. It's likely not for the reason that they desperately want to act for the good of the people.
Political parties in America don't have a traditional, singular "party leader" per se. The President, House Speaker (or Leader if the party does not hold speakership), and Senate Leader generally consider policies within their purview and consult with each other as necessary. A national committee governs a party outside of government.
Trump has an outsized presence and influence upon the Republican Party, both as President and as an ordinary American citizen, but this is rather unusual and not the norm.
The President is supposed to execute the laws faithfully. It's Congress' job to set policy. Not that it matters because we hav the Republican Party setting policy instead.