Elizabeth Willing Powel asked Benjamin Franklin as he exited the Constitutional Convention, in the then Pennsylvania State House (now known as Independence Hall), "Well, Doctor, what have we got, a republic or a monarchy?", to which Franklin replied: "A republic, if you can keep it."
The United States federal government is an intentionally complex organization. The only small-d democratic institution in the U.S. federal government is the House of Representatives. In the early years of the country, some states had all Representatives elected at-large, rather than from districts.
Originally Senators were elected by state legislatures. The famous "Lincoln-Douglas debates", where Abraham Lincoln was challenging incumbent Illinois senator Stephen Douglas, demonstrates this. Lincoln had won his party's nomination to be their Senate candidate. But the purpose of the debates was to encourage the citizens of Illinois to vote for their state representative candidate from the respective party of Lincoln or Douglas. It was not until the 17th Amendment was ratified in 1913 that Senators were directly elected.
Then obviously, the President is indirectly elected via the ephemeral Electoral College. Indirect elections of the head of government and head of state are actually the norm in most of the world. In parliamentary systems, the only people who directly elect the person who ultimately becomes the Prime Minister are those in that member's district. The head of state for a monarchy is not elected, and Viceroys or Governor Generals are appointed by the monarch, usually after nomination by the Prime Minister. For President-Prime Minister nations, often the President is indirectly elected, as in Germany.
In many parliamentary systems, the upper house is not democratically elected, but is appointed. However, in most parliamentary systems, the power of the upper house is severely limited. The upper houses of federal systems of Germany and Australia are similar to the U.S. Senate in structure, with some differences. France is a rare exception in that the President is directly elected, but he or she shares power with the Prime Minister, and the cabinet positions come from the parliament.
Obviously, the Supreme Court of the U.S. is not democratically elected. The three part of the U.S. federal government, the legislative, executive, and judiciary serve as checks and balances on each other. There is no small-d democratic ability for the people to recall a president, senator, or representative, like there is an ability to recall a governor in some states.
The Constitution's original design for the state legislatures to elect Senators was to address the Anti-Federalist's desire for the state governments to have influence. The 17th Amendment came about because of corruption. Senate candidates often were people who could get nominated and elected through graft, similar to how ambassadorships are nominated today. While that was a problem, unfortunately the solution, direct election of Senators, has turned the Senate into a sort of "Super Legislature", instead of a distinguished upper body.
My point is simple. The people who wail, gnash, and rend their garments over "Democracy!", and claim other countries are "more democratic", are little more than useful idiots with little understanding of how complex organizations work or how the rest of the world works. There are a lot of things we could do to make our system "more democratic" while not requiring significant changes to our basic structure. The U.S. House of Representatives has been stuck at 435 members since 1929. The U.S. population is now 2.75 times as large as it was in 1929. Expanding the House of Representatives would make the U.S. "more democratic." Maine and Nebraska apportion their Electoral College votes with one EC vote going to the presidential candidate who wins each congressional district and two EC votes going presidential candidate wins overall at the statewide level. If such a system were implemented across all of the states, large states like California, Texas, Florida, and New York would have significant EC votes in play for both parties, meaning California would matter for Republicans, and Texas would matter for Democrats. Instead of "Swing States" we would have "Swing Districts" where only one EC vote was in play, and "Swing States" where just two EC votes were in play. Presidential elections would suddenly become much more small-d democratic. Combine a much larger House of Representatives with a nationwide Maine-Nebraska EC model and the presidential election dynamics dramatically change.
There are other changes. In my opinion, the Senate has too much legislative power, and and as a result is too focused on legislation and not its advice and consent role. The entire Congress delegates too much power to the Executive branch. In hindsight, lifetime appointments of judges may not be the best approach. Vox media proposed an 18 year term, where two Supreme Court justice positions would expire during each four-year presidential term. Ending the judicial filibuster was a bad idea, but at the same time, the extreme partisanship around judicial appointees is worse. Senator's terribly worried about being primaried because they voted to approve a presidential appointment is one reason direct election of Senators has created new problems. Of course, if a president had to nominate a prospective justice who could get 60 votes, there should be fewer ideological challenges. But never forget, it was the Democrats who pilloried African-American Clarence Thomas, and filibustered Latino Miguel Estrada and African-American Janice Rogers Brown.
Ultimately, the answer for better, "more democratic" government is to reduce the centralized power and influence of the federal government in as many ways as possible. Federalism, subsidiarity, and localism are what makes democracy work. Putting more "democracy" in the central federal government will not make life better for the citizens. Potholes, traffic issues, crime, education, etc., these are local issues. Democracy starts at the city council member, not at the Senator or the President.
