Here's why that argument was undercut in Jefferson's own time
From the piece:
The Jeffersonians, among whom we for most purposes can count leading Framer James Madison, had an image in their minds of what government in general should be, which in a word one would say minimal. It was close to the ideal that libertarians still embrace today. We were to be a nation of independent yeoman farmers, each of whom looked after himself, and should the need for national defense arise, these doughty free men would come together spontaneously to drive away the invader.
Consequently, Jefferson opposed both a standing army and a navy, for anything other than coastal defense.
It is in that context that the Second Amendment makes the most sense. If those citizens were to be any use in a militia, they needed to be armed, and to have some personal experience with firearms.
But it didn’t take long at all for history to teach us the utter inadequacy of the Jeffersonian ideal of an armed citizenry being the only defense we needed. In Jefferson’s own time as president, he discovered the need to project power far beyond our coast, against the Barbary pirates. Our young Navy and its Marine contingent came in very handy in that instance.
But it took the War of 1812, “Mr. Madison’s War,” to demonstrate how useless untrained or lightly trained militia, with an unprofessional officer corps, was against the army of a superpower.