I think "adiós" as a greeting underpins the Spanish attitude to acknowledging other people.
Imagine you have ended up in a Spanish social situation with quite a lot of people in a room. The person you are with will introduce you to everyone - one by one. If you're a man you shake hands with other men and do the two cheek kissing thing with all the women. Women do the two cheek kisses with everyone. For a street meeting with a friend who introduces you to their boyfriend/girlfriend/partner/mother in law and so on you'd do the greetings just the same. If the meeting were brief, a few moments, you might need to follow the same ritual for goodbye.
On entering a public space it's not at all unusual to give a general greeting to everyone. We were on a trip to Italy with a bunch of Spanish people and the majority of people greeted the other coach passengers with a cheery "Buenos días" as they breasted the top of the stairs to get on the bus. The same happens when people walk into the Post Office, a bank or a bar. The majority of Spanish people say hello to everyone by launching their greeting at nobody in particular. Equally as you're about to leave the bar or a restaurant it's not at all unusual to let fly a cheery goodbye, hasta luego or adiós, into the ether. Indeed if you're in a restaurant you can be a bit more specific and direct a “que aproveche”or “buen provecho" at other diners as you pass - it's a Spanish version of bon appetit and though grammatical purists complain about the phrases it's what people say.
I was reminded of this determination to acknowledge other people just before Christmas when I made a terrible mistake and signed up for a walk to the top of el Cid, the flat topped mountain on the border between Petrer and Monforte del Cid. My lungs are scarred from 40 years of smoking cigars and I could hardly breathe from the first steps out of the car park to the moment when we reached our goal - eating our sandwiches on the summit. It's apparently a bit of a Christmas tradition in Petrer to go up the mountain in festive clothing so there were all sorts of runners and walkers sporting Santa hats and reindeer antlers up and down the path as I panted and gasped upwards. I was pretty much centred on keeping breathing to stay alive but I swear that every damned person who passed said hello or good day or some such to me and to the every individual in the group. I did my best to bleat out a response.
I am particularly gormless in almost any social interaction. I much prefer to keep a low profile and I can never bring myself to do this greeting the whole room thing, even when I remember it's what should be done. I'm even more inept at the two cheeks kissing with women. Getting that close to a woman I hardly know is very near to sexual harassment in my old fashioned play book. This causes me a minor problem in Spain when I hesitate to go around, for instance the people from the neighbourhood association, air kissing and hand shaking. They expect it, to them it's normal, I don't do it and so, in their minds, I become a standoffish foreigner. It's difficult to teach an old dog new tricks though and, for years, I have greeted even my closest family members with a little nod, a shrug of the shoulders and a vague (Yorkshire) greeting "a'reet?"