People are also creatures of habit
I've got a different take on Butts' question, but while we're talking about coincidentally meeting people we know, or our restricted sphere of contacts due to our habitual patterns, then I must say that I am 'accused' of knowing people everywhere I go. I do seem to encounter people I know a lot, in other cities, in quite unlikely places.
. . .it's all the more funny when you do recognise someone.
My particular 'funny' experience of encounters is skewed by having 3 'doubles' with whom I am very regularly mistaken, even after quite prolonged conversations. I have learned quite a lot about these other individuals from the people who mistake me for them (one of them is professionally connected to railway personnel). One consequence of this strange mistake is that more people greet me as a friend / aquaintance / professional contact than the number of people who actually do know me. As this has been going on for many years, and the others are ageing in similar ways, the confusion is only stregthened by the passage of time.
I wonder how many people we see in a lifetime only once and never again.
But my take on your question is to question the value we place on the fleeting, but probably never to be repeated, glimpse of another person. I am sympathetic to that thought. But as it is a thought about the passing experience, rather than a thought about the relationship with the person, then I would say that the essence of the question is about the significance which we attach to our experiences - ranging from being oblivious to them (experiences or other people), through to being entirely consumed by them. [I don't know a thing about 'mindfulness', but isn't this question in that territory?]. If all that you have to say about the people in your question is that we have a glimpse, that it is feeling, that it is probably never repeated, then I have to ask if that instant is of any significane at all other than as an image? (or scent, or sound)?
Often, I do regret failing to observe something - whether it's in the natural world or the human world (e.g. Why haven't I noticed the kingfisher or otter in the local river for the last few months? Or, why didn't I recognise exactly what a friend had just done to their appearance? Or, why hadn't I noticed that the new moon had appeared? Or, why hadn't I realised that I hadn't seen a neighbour, whom I like to talk to, for a few weeks?).
I regret failing to notice changes (whether in the human or natural world) but I don't regret not seeing again people or things which I encounter once. It's one reason why I haven't bothered to buy a digital camera (I was an enthusiastic photographer for a while in the days of film). If I can't keep an experience of a person alive in my mind (or of a thing), then I don't think that a photo of them is really going to help my relationship with them. And if it's a thing, then it wouldn't be a relationship.