DNS changes propagate. They just do-so in a pull, not push, way.
It’s accurate to say that a user is waiting for the change to propagate if they are sitting there clicking re-try as they wait for the cascading cache expirations to do their thing.
Yes! The idea of DNS records "propagating" gave me entirely the wrong mental model of DNS very early in my career. Granted, the confusion didn't last long because I read the cricket book soon after, but it was still pretty jarring.