Ray, I think that in most cases people fly from their home country to one destination, then back. At check in the staff will know, from experience, if a visa is required or not. If required, a quick check is made, often without you knowing. Because I travel a lot, and I mean a lot, I am often flying from my none home country, or place of residence, to another, separate destination. Made even more complicated by having residency in a place that is not my country of origin...... So, examples, flying from, say, New York/LA, or Paris/Frankfurt/London to Hong Kong, (which I do a lot), I have to show my Hong Kong residents card and my visa. Even though I get by rights, on the passport I travel on, 3 months stay. Same if I am going to China, India etc. So I often have to explain, or wait while the person checks. Probably one in ten, one in twenty flights. Varies.
Can be interesting watching the expression on peoples faces as they go through my passport looking at all the pages full of visas .......... and the "oh, I have always wanted to to visit ......, what is it like?" comments.
And, not speaking from personal experience, but I think I would like to know before I get on a plane if I actually need a visa for a place rather than getting an "entry refused" stamp in my passport.