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They actually argued against that, saying that disciplining "all the militia" would be "as futile as it would be injurious". They preferred a select state Militia, amounting to less than 20% of the population.

You are referencing Federalist 29, written by Hamilton, who was the biggest big government guy of his day. Others didn't feel the same way. You've also mischaracterized what Hamilton said.

"The project of disciplining all the militia of the United States is as futile as it would be injurious, if it were capable of being carried into execution. A tolerable expertness in military movements is a business that requires time and practice. It is not a day, or even a week, that will suffice for the attainment of it. To oblige the great body of the yeomanry, and of the other classes of the citizens, to be under arms for the purpose of going through military exercises and evolutions, as often as might be necessary to acquire the degree of perfection which would entitle them to the character of a well-regulated militia, would be a real grievance to the people, and a serious public inconvenience and loss. It would form an annual deduction from the productive labor of the country, to an amount which, calculating upon the present numbers of the people, would not fall far short of the whole expense of the civil establishments of all the States. To attempt a thing which would abridge the mass of labor and industry to so considerable an extent, would be unwise: and the experiment, if made, could not succeed, because it would not long be endured. Little more can reasonably be aimed at, with respect to the people at large, than to have them properly armed and equipped; and in order to see that this be not neglected, it will be necessary to assemble them once or twice in the course of a year.

"But though the scheme of disciplining the whole nation must be abandoned as mischievous or impracticable; yet it is a matter of the utmost importance that a well-digested plan should, as soon as possible, be adopted for the proper establishment of the militia. The attention of the government ought particularly to be directed to the formation of a select corps of moderate extent, upon such principles as will really fit them for service in case of need.

It looks to me like Hamilton hoped that the people at large should be properly armed, and ALSO that a select corps would be formed and given military training. That idea was treated with suspicion by anti-federalists, as evidenced by Hamilton saying this in Federalist 29:

It is observed that select corps may be formed, composed of the young and ardent, who may be rendered subservient to the views of arbitrary power.

"Little more can reasonably be aimed at, with respect to the people at large, than to have them properly armed and equipped"

"The people at large" were the Militia, and they were to be assembled "once or twice in the course of a year". He wasn't suggesting asembling every person in the United States once or twice a year.

So, even though all of the people would be armed, it made sense to only organize a certain part of them. Like, men of fighting age, perhaps? As paulsen obfuscates. Some of "the people" would be part of the "organized" militia, everyone else would constitute the "unorganized" militia.

Of course, paulsen will point to some Jim Crow court to prove that not everyone is a "people" but I think we have resolved that issue over the years, much to bobbys dispair.