Are cashiers in the United States of America really required to initiate meaningless conversations? I’ve also heard of the occupation of a door greater, which sounds even crazier.

The corporate ideal has their weird idea that everyone desperately wants to have conversations with employees. I think it comes from positive feedback often taking the form of, "Your employee was so warm and helpful and we had a delightful chat about X." and never, "Your employee was polite and didn't bother me with needless conversation." One of the trainings my employer has even includes a scenario, which is presented as ideal service, where the employee ends up chatting with a complete stranger about his dead wife including sharing pictures from his wallet.

That said, while I'm sure corporate cares none of my in store managers cared when I was a cashier. Indeed, I had regulars who would seek me out because I specifically didn't attempt to inject small talk into the interaction. I'd still get pulled into it by customers who initiated such but otherwise it was mostly, "Morning. Coupons? That'll be $X.XX. Have a good one."