You seem to be ignoring the concept of an armory (the local Armory food hall used to hold weapons) which does not require individual ownership of the heavy arms, not a standing army.

Also there is no "no sanding Army" requirement. There is only a requirement that the army can only be funded for 2 years ahead, presumably to require ongoing consent from Legislature, to prevent a Chancellor Hitler-type situation or a President becoming King by getting a huge multi year funding and then turning against the future Legislature and the country.