As far as the "no weapons that aren't on the House Weapons List", that only implies at startup. It is meant to coral some of the min maxing that bleeds some of the fun out of trying to keep your gang standing let alone fighting, so to me is meant more to influence lore considerations when building a gang on what sort of kit your characters are likely to have rather than what possible tactical approach options you could make if you were to utilize a weapon off the list here or there in roles. In either regard, the House Weapons List stipulations are like the Leader Only Weapons, and they melt back into the gang's supply feed after the first game. Which is a weird little roundabout, but a means of further suggesting beyond skill trees a House's dynamic through its typical weapons kit.