The “rep” of republic has no etymological relationship to the “rep” of representative. It’s just a coincidence.
Well that shows me for making assumptions. 
Works out handily though.
It is technically correct. There is no requirement that democracy mean “direct democracy.” And one can have a non-democratic republic. In fact, that pretty much describes all republics prior to the U.S., as it was apparently Madison who came up with the idea of a democratic republic and defined it to mean a representative democracy.
All that is required for a republic is that you have some political body that is supposed to represent the people, voting among themselves on how to govern. It is not required that they be elected. The Roman Senate was originally appointed by the king or consul and were just the heads of the the important families. Yet we call the government where the Senate had primary legal power the “Roman Republic.”
The U.S. is an indirect, representative democracy that takes on the form of an liberal democratic republic. It was effectively an experiment by its founders, as that particular form of government had never existed before.
That’s why it didn’t happen back in England. This new type of democracy just had not been considered. It is, as someone else pointed out, an idea that came out of the Enlightenment.
What’s the link between Presbyterianism and the enlightenment ?
Government by elected official, rather than by hereditary ruler was not. Even if the modern idea of a liberal democracy
It was there in the ideas of the Agitators and other radicals in the English Civil War
*That the power of this [a regularly-elected, fixed term, parliament] * and all future representatives of this nation is inferior only to theirs who choose them , and doth extend, without the consent or concurrence of any other person or persons, to the enacting, altering, and repealing of laws; to the erecting and abolishing of offices and courts; to the appointing, removing, and calling to account magistrates and officers of all degrees; to the making war and peace; to the treating with foreign states; and generally, to whatsoever is not expressly or impliedly reserved by the represented to themselves.
(An Agreement of the People, October 1647).
But the argument that won (because Parliament had the power, the money and the generals) was that stability demanded representation only of those with a fixed property interest - and it seems from previous posts that that idea clung on in the young United States.
It is noticeable that the radicals of the English Civil War did not envisage a separately elected President, merely a Parliament. What did for the Commonwealth regime was that it did not provide for its own renewal through electing a new parliament, because it insisted on such a degree of ideological purity that it did not allow free elections. And it would seem no-one could envisage a regime without some sort of powerful leader, but in the end there was none obviously to hand but Charles II.
There are many reasons why the English Civil War broke out and one of the most significant is religion. The Church of England was a broad house at the time and incorporated many differing opinions, the King and Laud being the Arminian, high church, Anglo-Catholic branch, and parliament having a health strain of energetic, low-church presbyterians. Religion permeated everything - there were riots and fights over what direction altars were facing, for Pete’s sake - including sports, economics, and foreign policy. One of the reasons why the English never got involved in the Thirty Years War was because the King favoured the Spanish (who let the English mint his silver, meaning lots of cash for London), while most others wanted an alliance with the Dutch and French.
Anyway, the chief bone of contention vis-a-vis democracy in the English Civil War (and the Scottish, for that matter) was about democracy in religion. Religion was such an enormously important and all-encompassing matter that everything was viewed through that prism. They had concerns about public control over secular institutions too, but it motivated them far less than public influence into their own faith,
Anyway, Cromwell’s New Model Army tipped the scales in Parliament’s favour, but in doing so tapped into the power of the ordinary folk. In the desperation of 1643-44, when Parliament lost nearly every major battle, it was forced to innovate in ways it would never have contemplated before, and to commit outrages worse than the king had been condemned for. In the process, parliament ignited a new radicalism - the Independents.
For many in England’s army in late 1648/early 1649, the king represented all that had gone wrong in England in the 1630s and 40s, and he had to die. But that’s as far as the radicalism of some MP’s radicalism went. The republican Commonwealth’s founding fathers were, arguably, the least enthusiastic republicans in history.
But the army, which had grown powerful, radical, and political, held parliament at its mercy, and it demanded the king’s death. It was also mostly dominated by Independents, with Cromwell at its head, and so religious liberty was a cornerstone of their demands. Beyond that - demands of political liberty and the right to decide their own government - there were as many points of view as there were people. They simply could not agree on what the Commonwealth was for. And so, by sheer inertia, and the shock victories in the Third English Civil War, the Commonwealth endured until Cromwell dissolved it in 1653.
Cromwell became Lord Protector, but while radical in religion, he, like the overwhelming majority of Englishmen, was a political conservative, although prone to poorly-considered bouts of religio-political radicalism at rash moments (Rule of the Major-Generals, anyone?). When he died, the one thing that held the regime together faded away with him, and shortly after all the arguments and disagreements that had been stilled by Cromwell came back to the fore.
For all the monarchy’s faults, at least it gave firm direction, was one of the reasons why the monarchy was restored. Basically, Parliament wasn’t that interested in political freedom initially, but was forced to consider it by the army, although it did its level best to drag its heels on the issue as much as it could.
I got that slightly wrong. At the end of the interregnum, there were contenders for the strong man/Lord Protector job, the chief bone of contention being that the government was in debt, mainly for Army pay, the Army wanted a continued say, and Richard Cromwell, as a civilian who hadn’t exactly been a powerful figure in his father’s time, simply wasn’t rated by the Army leaders. There were parliaments in these last years, and more than one Army general who made a bid for power, but they couldn’t agree among themselves who should be in charge or with what objectives, and in the end Monck and his army simply forced the issue.
Hey OP, I just started reading The History of the Commonwealth and Protectorate by Samuel Rawson Gardiner, published 1901. The opening words seem to sum up why the English Commonwealth was a failure pretty succinctly: