On the other hand, I've worn work boots since high school, and wouldn't give them up. (Literally! Uniform required penny loafers or better. I got chewed out more times...) Callused soles won't save you on sun-hot asphalt or gravel, and knowing what you're stepping on won't do you a lick of good when 120 pounds of server and handcart run over your toes.
Broken glass is far more common in modern times than it was on the savanna, so it's wise to dress accordingly. You don't have to wear Dr Martens, but a millimeter or two of Vibram can dramatically improve your quality of life.
From personal experience, it takes quite the sharps to cut through 10-12mm calluses.
As a manager, I wouldn't be worried about them being worried. I'd be worried about them suing the company if they injure their foot.
Unless they're encumbered with a 80-pound piece of furniture that they're carrying down the stairs.
Putting rigid shoes on your feet is like stuffing your nose with cotton - you're completely blocking a very sensitive organ to the rest of the world.
All this just to say: people who walk barefoot every day are not worried of stepping on tacks :)