Random greeters slightly annoy me....it seems phony & serves no real purpose from my perspective. If I want help, I will find someone & ask. An exception to this is in a clothing store, because I appreciate when they start a dressing room for me (when I have an armload of stuff that is), but I don't want to be nagged into anything either. And that said, it's not any major annoyance - very easy to ignore.
However, when I am dealing directly with someone (ie. a bank teller or cashier), I prefer some basic politeness to being overly blunt. I don't like the talk to become too lengthy or personal though. A mere "Hi, how are you?" works with a pleasant face, demeanor & tone of voice. I don't like to feel like I am bothering them, basically (I've seen employees make customers feel like burdens...).
It certainly doesn't "brighten my day" if I am in a bad mood though. In fact, if I am in a bad mood, and respond briefly to any inquiry, I hate when a happy-go-lucky customer service person tries to push their happy talk on me.
When I've worked in retail, I was actually pretty good at picking up on whether a person wanted pleasant small talk at the register or not. It's easy to smile, be open, and let the customer decide how much talk they want.
Anyway, I will choose "no small talk", because politeness is more than enough for me. Chitchat is not necessary.