Arsenals were definitely run by the government and are even referenced within the Constitution. One of the first projects of the new nation was to set up manufacturing capabilities for armaments and military equipment. During the Civil War even the Confederacy established government run factories to produce artillery. The Springfield Arsenal is world famous for the guns it produced.
No matter what Franklin was to do, artillery not stored in private homes nor owned by private individuals or groups.
Artillery was extremely unwieldy and hard to move especially if the weather had any wetness or the ground was wet. It was not of use in pursuing Indians, in fact, it was worse than useless in those cases because it slowed down any unit to a crawl.
Alexander Hamilton first came to Washington's attention when he was an teenage officer in a New York artillery company. The state required mathematical knowledge to receive his commission. That was standard at the time of the Revolution which is the period I am speaking of. Mathematics was a necessity for any aiming other than just pointing in a general direction and firing.
Ask a bellmaker how he would make a blackpowder cannon. Your average blacksmith probably could figure it out. Back then, anything metal was handmade by the local smith.
Your assertion that only government agencies had them is just preposterous.
"Arsenals were definitely run by the government"You are forgetting the govm't was King George and the boys. After the war Congress established arsenals... ect to scale with their new condition. THey did not replace private sources, or eliminate private holdings. Not until FDR did the US start to disarm their citizens. Until that time all manner of arms were available.
"artillery not stored in private homes nor owned by private individuals or groups."
No one stores cannons in their home. They go in the workshop. The gun owners shop.
"Artillery was extremely unwieldy and hard to move especially if the weather had any wetness...
Yea, mud. I'm well aware of moving and shooting cannons. I've done it under the same conditions. With imaginary opponents of course.
"Hamilton"
Officers train juniors, that train sgts, that train crews. Once in the field it's the sgts gun and the shooting is directed by the officer in charge, but done by the sgts and their crews.