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In America, probably yes. I don't suppose there's a cop in the US who doesn't carry a gun. However the whole country seems to have the same gun culture, cop or not. If this same scenario played out in the UK the kid would have got to the shop, done his business and been given a carrier bag to carry it away in. The concerned off duty security guard would have phoned it in and if the unarmed police had got there they would have observed from a safe distance. Inquiries in the shop made and everyone goes home safe. In an ideal world that's what would happen but if UK armed cops had turned up I doubt the kid would have been shot. UK armed cops are trained to de-escalate as soon as practicable and are in pairs whenever possible. The untrained fuckwit with a gun scenario would not happen in the UK.
Isn't it often more than that though? You like the idea of hitting nails, so you buy lots of different hammers and hammer-adjacent items, and then go looking for nails or nail-adjacent or anything that looks nail-like in the dark through squinted eyes, and then hit away as soon as the opportunity arises.