Federalist 51
> The interest of the man must be connected with the constitutional rights of the place. It may be a reflection on human nature, that such devices should be necessary to control the abuses of government. But what is government itself, but the greatest of all reflections on human nature? If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself.
> A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions. This policy of supplying, by opposite and rival interests, the defect of better motives, might be traced through the whole system of human affairs, private as well as public. ... But it is not possible to give to each department an equal power of self-defense. ...The remedy for this inconveniency is to divide the legislature into different branches; and to render them, by different modes of election and different principles of action, as little connected with each other as the nature of their common functions and their common dependence on the society will admit. It may even be necessary to guard against dangerous encroachments by still further precautions. As the weight of the legislative authority requires that it should be thus divided, the weakness of the executive may require, on the other hand, that it should be fortified.
This right here is talking about why there is the separation of powers. This is the reason judges are supposed to be without party. But we all know that this is a facade. But of course it is, when we see how these judges are appointed. How could it be any other way? The recognition here is that there are no perfect solutions as to optimize towards one thing results in a worse outcome (see the other parts of the writing).
I think not enough people have read the Federalist papers. They are an important context to why the US was founded and what problems it was trying to solve. Littered throughout them are discussions of how power creeps and how functions couple. How government can do great good but at the same time great harm. They reiterate the notion that liberty is hard work and many of the writers fear things like parties as they are not only concentrations of power but umbrellas to remove thinking. You can see them wrestle with ideas and that they know they aren't getting them right, but instead try to set a framework that can course correct to adapt to the unknown unknowns.
But however you read them, I think you can and will read that such a conclusion is precisely the thing they were trying to stop. There is no ambiguity in this. They were fighting against monarchs who have written into the law that they are above the law. At least as it pertains to others. And so that's what that phrase means "no one is above the law" that not so literally (because making a law that makes special cases for you would not technically make you "above" the law, but part of it), but rather that the laws apply equally to all peoples and entities. That there are no special cases because there are no "to big to fail" and "too important to prosecute". Because the belief is that if it is wrong for one man to commit an act, then it is wrong for any man to commit such an act.
[0] Federalist 51: https://avalon.law.yale.edu/18th_century/fed51.asp