the people are the militia"
No, the Militia Acts make only a subset of the people the Militia.
The Militia Acts declare who are the militia. Acts written by the Congress, representatives of the people, using the powers invested in the them by the people:
"The Congress shall have Power...To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;"
"Amendment X
The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.
Now, no doubt Congress could abuse this power, and through usurption(?), render the Militias useless:
"Mr. Gerry.--This declaration of rights, I take it, is intended to secure the people against the mal-administration of the Government; if we could suppose that, in all cases, the rights of the people would be attended to, the occasion for guards of this kind would be removed. Now, I am apprehensive, sir, that this clause would give an opportunity to the people in power to destroy the constitution itself. They can declare who are those religiously scrupulous, and prevent them from bearing arms.
What, sir, is the use of a militia? It is to prevent the establishment of a standing army, the bane of liberty. Now, it must be evident, that, under this provision, together with their other powers, Congress could take such measures with respect to a militia, as to make a standing army necessary. Whenever Governments mean to invade the rights and liberties of the people, they always attempt to destroy the militia, in order to raise an army upon their ruins."
Hence the final wording and primary purpose of the 2nd declaring the well-regulated State Militias as necessary, and once again securing the rights of the people (who of course would serve) to arms.
Of course - now, the Congress, still invested with power by the people, define the militia as:
(a) The militia of the United States consists of all able-bodied males at least 17 years of age and, except as provided in section 313 of title 32, under 45 years of age who are, or who have made a declaration of intention to become, citizens of the United States and of female citizens of the United States who are members of the National Guard.
(b) The classes of the militia are
(1) the organized militia, which consists of the National Guard and the Naval Militia; and
(2) the unorganized militia, which consists of the members of the militia who are not members of the National Guard or the Naval Militia.