Hamilton didn't believe that. In fact, he argued against it in Federalist 29:
"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."
"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 ..."
Which is why the second amendment says that a well regulated Militia is necessary to the security of a free State, not that a well armed citizenry is necessary to the security of a free State.
"The idea behind a citizen’s militia was that every able-bodied adult male in the country was a part of it."
In 1788, the idea behind a citizen’s militia was that every able-bodied adult white male citizen in the country was a part of it. Which was less than 20% of the population at the time.
Not even close to "everyone".
And that's just his point #1. Posting the link large and blue doesn't make it right.