Def not goofy. For one thing, think about this - good construction tools are expensive so a construction site during work hours is a collection spot for thousands of dollar's worth of equipment. Good place to pick up something worth some cash, if you're not above stealing. However, construction site is also a collection spot for bit, strappin' construction workers. Not the kind of guys you'd want to mess with. If I was intent on stealing some goodies, I'd be armed.
Yeah, I'd carry! And yes, I've done construction work.
~Dale