I agree with you that an armed populace is one factor that supports democracy

In fact, I believe that the invention of firearms democratized military might by making the professional soldier (knight, man-at-arms or Swiss style mercernary) obsolete. In a time where military might was determined by how many men could be drafted into service, a government could only retain power through the support of those drafted men.

A rule by "all drafted men", in other words, is the foundation of democracy. Like most societies, a democracy is rule by the predominant warrior caste. In the greek democracies, all male citizens were serving as hoplites. That was teh basis for their "democracy". The Roman republic had legions of citizens (until Marius), enabling another form of citizen rule. Then came the Marian reforms, with professional soldiers controlled by the elite. Almost directly after, Sulla, Caesar and Octavian introduced the Roman Empire.

500 years later, the Romans in Western Europe were overrun by Germanic chiefs. Their elite soldiers became the armored knights of the Medieval Europe, and they introduced Feudalism, where power was held by the nobility (and sometimes shared with a king, who was often quite weak).

Then came the age of the pike armed Swiss mercenaries and similar non-noble military formations more similar to the legions of Imperial Rome. This gave many European monarchs full controls.

The founding fathers saw this, and rightly predicted that armed citizens was an ingredient in ensuring governance by the people. In Europe it would take another 150 years or so for this to play out.

Many on the left will not realize this. They think that democracy is self-sustaining regardless of potential for the elites to be corrupted and sieze the power.

The founding fathers had studied their history. They knew about Marius and Sulla and how the Roman elites quickly had taken control once the citizens were no longer the backbone of the army.

The founding fathers were not "common people", but rather highly educated members of the elites. Their existence had been made possible by a monarchical system, and they bore many similarities with the elites of the Roman empire (the senators).

The guns may give the power to rule, but not the wisdom, and people like Thomas Jefferson understood this. And this is where the understanding of the populist right falls short.

Thomas Jefferson in particular was a proponent of quality education for the citizenry, he thought that "no other sure foundation can be devised for the preservation of freedom and happiness".

In other words, not only guns but also books were needed to keep the people free (and happy).

https://en.wikipedia.org/wiki/Thomas_Jefferson_and_education

When citizens completely lose the ability to understand the world in which they live. He promoted the teaching of "Science and Virtue", but was concerned about intellectuals from "tyrannies" in Europe.

Maybe he anticipated something like the Frankfurt School?

The only way to prevent demagogues (like Ceasar) who promise to people that which is impossible to deliver, is to:
1) Make sure the people know enough Science to be able to know the possible from the impossible.
2) Make sure people know enough history to recognize what values are true Virtues that lead to healthy societies, and which are hollow lies, more suitable for use by would-be-dictators to gain control.