Greeting the greeter
The past few "greeters" I've encountered as I've walked into big stores have not greeted me. I've initiated the greeting. Just seems odd!
From a language standpoint, greetings are a "couplet." There's the first offering (from person 1), e.g., Hello, Good morning, etc., and the second part, or "person 2's" reply, Hi, How are you, etc.
It's almost a reflex for person 2 to reply, once the first phrase is offered. In the case of a greeting at a store entrance, it engages the customer, it makes you feel less anonymous, and presumably personalizes your shopping experience.
But...if I'm the one doing the greeting (as the customer), I don't know if that's the case!