No offense taken, this is an interesting thread; I never thought it annoyed people when it WASN'T hatefully inspired! Usually when people leave my store I am genuinely hoping they have a nice day, because the area is beautiful and it's so easy to find something great to do. On the other hand...
When someone is screaming at me because I wouldn't take their expired coupon, or because I wouldn't give them cash back on a return when they didn't have their receipt, or because they tried to return 2-year-old nasty sneakers that "didn't hold up well," after I have tried politely explaining what I could do (never using the phrase "I can't" ) and telling them I understand they're frustrated but..., they're going to get a little bit of sarcasm. It may not be good business, and it might piss people off, but it's better my temper comes out subtly there than I end up screaming back at them.
"I'm sorry you feel that way" only fires some people up more. Usually I am NOT sorry they feel that way; I am pissed off as hell that they're screaming at me for following rules I did not make. That technically equates it with the fake "Have a nice day." It's not about being questioned over money, it's about people treating people like absolute crap just because they're on the other side of the counter and thinking it's perfectly fine.
I have had stupid cashiers work for me (I have BEEN a stupid cashier, too, I confess!). These people don't last long (I didn't). Most cashiers are NOT stupid (I got better), they are typically students trying to earn some money for books, rent, booze, whatever, it doesn't really matter; they're not schmoozing off their parents while they're learning responsibility, and they handle an enormous amount of cash, checks, and credit cards on a daily basis, so they should be given more credit than they usually are by the general public.
A lot of places require you to greet people, too. I hate when "Hi, how are you? Hi, how ya doin'? How's everyone today?" becomes monotonous, but that's my job. Our customers are surveyed on their in-store experience and if they're not all greeted, we lose points, and I don't get a raise. If people don't answer me, I will follow them around the store until they do.