If your police department can have a weapon, then your neighbor should be able to keep the same weapons.
Let me key on the "well regulated" bit for a moment. We have lost something in the past hundred or so years. We don't have hometown mlitias any more. If you should read some of the stories of units that fought in the Civil War, you will find that many soldiers fought and died with the boys they grew up with, and the elders from their own home towns. That is, the county more or less maintained it's own militia, which volunteered for service to the state in times of need. Or, in the case of the Civil War, they volunteered, as a unit, with the US Army.
So, these militias were drilling on the town square routinely, each and every year.
You have a point - the individual militiamen didn't take cannon home with them. Or gatling guns, either. They may or may not have taken their rifles (or muskets) home with them, depending on whether they bought the weapons with personal funds, or were issued by the county or state.
BUT - wherever the cannon, the gatling guns, and the government-owned small arms might have been stowed, the militia had ready access.
I'm kinda getting off of my central point though. Well regulated. At age 17, boys were expected to muster with the militia for training and drill. They were expected to continue doing so, until about age 40. And, thoughout their adult lives, they were expected to be ready for action.
Well regulated? Of COURSE they were well regulated. If the commanding officer happens to be your best buddy's grandfather, and the adjutant is your second cousin by marriage, and you went to school with all the privates, your dad is a corporal - yeah, you bet your ass that you'll stay well regulated! No way are you going to go home in disgrace, with all your freinds and family mocking you for the rest of your life!
Of equal importance - these militias were not units of the US Army, or even of the individual state's "National Guard". They were independent units, ready to respond to emergencies of any kind. They often did volunteer for service to the state, or service to the Army, but they weren't actually obligated to do so.