Correct, but not for the reasons you list. The Second Amendment is about the balance of power between the government and the citizens. The Founding Fathers knew that if the government had all the guns, the citizens would have no protection against an abusive and runaway central government.
Also, in the days of our nation's founding, militia's were comprised of citizen soldiers. During times of national emergencies, there would not be time for these citizens to go to a central armory to withdraw a weapon.
And we know what happened in that case.
I'll simply have to disagree with you on that. What I wrote in whole was correct. What I didn't write was, and what you wrote, about the central reason of the 2nd Amendment.