Doing it seriously takes real work.
Yes, that's exactly right. That's what the above is. You have to maintain polite contact with people in order to stay on the radar. It's why people used to send each other Christmas cards even though they had not spoken all year. Just touching base, letting you know you're still on my list.
None of the above imagined conversation is to be taken literally. It's just a polite ping/ack. It doesn't create any further obligation.
I used to believe that whenever coworkers ask how to stay in touch after I leave a job it was just a lie we all tell ourselves to make the transition easier. But I'm finding that many of my coworkers say they do stay in touch with old colleagues.
Perhaps part of the lesson is that some of us who don't reciprocate with you do care, but have no mental model (or lack the social grace) to navigate a more tricky relationship (e.g. what if work is now much better now that this person left, and what if the people and things you had in common no longer apply).