You remember the separation of powers, from that High School Civics class? If not, you are not alone. Even Senate Majority leader Mitch McConnell appears to have forgotten. So here's a brief review, for you and Mr. McConnell.
The founders of the United States were great admirers of the balance they saw in the government of Great Britain. Their admiration for the British system continued after the American Revolution. When they sat down to create new governments (both at the state and eventually at the federal level) they tried to adapt what they saw as the strengths of the British system to their own circumstances. Their revolution broke the tie to monarchy and their society had no equivalent to the hereditary nobility that sat in the House of Lords. Working within these differences, they tried to recreate what they valued most: the Separation of Powers.
According to British Constitutional theory, that government worked by balancing social and political forces. The royal family, represented in the monarchy, then had a role to play in governance; the House of Lords represented the aristocratic elite in both church and state (the Church of England's highest officials sat among the nobility); and the landowning elite was represented in the House of Commons. (The vast majority of adult Britons had no political role to play, either because they owned insufficient property to qualify or they were women.) American political thinkers, admiring this balance, thought they should create a government that similarly separated powers. The three parts of the federal government: executive, legislative and judicial, was seen as one way to create this separation.
The desire for balance created a conundrum for the founders. With only the people (no monarchy, no hereditary elite) upon which to erect their government, they came up with various plans to ensure separation. The way elected officials were appointed was intended to remove the process of selection gradually from the people. Voters directly elected representatives to sit in the lower house; (hence the name "representative"). States were to select Senators--so voters elected state legislators who then selected Senators; this provision was done away with a century ago, in the Seventeenth Amendment, so we have directly elected Senators since 1913.
The need to separate the people further from the process of choosing the President gave rise to the much maligned Electoral College. Voters in each states choose delegates who sit in the Electoral College and there select the President. This system, which can result in cases when the popular vote for President differs markedly from the Electoral College outcome, earns criticism for being convoluted and removed from the will of the people. Such criticisms reject what the founders' aimed to accomplish.
Which brings us to the Supreme Court. The Constitution looked to the least democratically-elected public official, the President, who was thought to be most removed from politics, to appoint Supreme Court Justices. In making that selection, the President consulted with the Senate, the second most removed elected body (and one that was supposedly protected further from politics by standing for office only ever six years). The idea was most emphatically NOT to "let the people decide." The entire system was designed to remove the Court from the messy reality of politics, putting it into the hands of the more dignified and removed President and, to a lesser extent, the Senate.
Mitch McConnell has recently and repeatedly stated that the people ought to select next Supreme Court Justice, by which he means that the Senate will not consult over an appointment until another Presidential election has taken place. While "let the people decide" has a nice ring, by using it McConnell shows his ignorance (or his willful disregard) of the founders' intention. He also well demonstrates the Senate's descent into politics. The founders sought to avoid this problem, hoping to create a system that would avoid a Senate leader more dedicated to his party's fortunes or any particular political program than to the smooth functioning of the government.