And if your interpretation was correct, our Founders could very easily have limited the second amendment to, "The right of citizens to keep and bear arms shall not be infringed."
But they didn't.
(Oh, and it's not "state-regulated militias". It's well regulated state Militias. Congress has the power to organize, arm, and discipline the state Militias.
From a grammatical standpoint, the Second Amendment says just that and more. Anti-gunners would take the simpler version and trot out their "the Constitution is not a suicide pact" to claim that people do not have the right to arms which threaten the state.
The history of the Revolution makes clear that the arming of the general populace was an issue of extreme importance. The occupiers of Boston demanded that people surrender their arms as a price for being allowed to leave Boston with their other goods. These were not just people who were in an organized militia.
Nope, doesn't say that. It says "well regulated militias", the state part comes afterwords, and in such a manner as to be interpreted to mean "government" or "country", not one of the Several States. But in any case, in the second amendment's single sentence, "state" is not an adjective modifying "militia".
So why did they put in an amendment saying, according to your interpretation, the same thing.
BTW, it's a power to "provide for" arming the militia. In the event, they provided for it by having the militiamen bring their own private arms to the party, and by defining what those arms would be, without limiting what additional arms the militiaman could own, or bring for that matter, they just provided a minimum standard. That standard even included pistols as a requirement for the member of some types of units.