You are conveniently only citing Heraclitus for his observation of change/flux, but missing his point in doing so. Why do you think he mentions the river being the same? From what we can re-construct from his fragments, his philosophy was about discovering permanence within change.
The original fragment emphasizes the changing material of the river while implying a persistent identity of the river itself, rather than advocating for some chaotic flux. I keep seeing people mischaracterizing Heraclitus as some philosopher of pure, unending change, and this is likely driven by projecting modern existentialist/nihilist(yolo framework) onto him.
For him, the Logos, which is a deeper, eternal unity of opposites, could be reached through resolving contradictions found within change and looking for what observes change- not dissimilar to what Vedantins in India still do when they re-direct their attention from ever changing thoughts to the observer of the thoughts.
Your argument here assumes that rebirth- if its happens- is some kind of total reset where nothing carries over except for some vague spirit.
That contradicts both the traditions that gave rise to the concept of rebirth and newer Western studies on reincarnation.
Professor Ian Stevenson of the Uni of Virginia spent some four decades on verifying memories of young children- memories they could not possibly have had if they had no access to a previous life-
he documented cases where children recalled verifiable details of a deceased strangerās life, had unusually developed abilities, bore birthmarks matching their previous incarnationās fatal wounds, or exhibited specific phobias directly tied to the manner of death. And these are only the surface indicators of the transfer of information across lifetimes.
What he did is only part of mounting research on similar cases- there is also interesting case studies in past life regressions. Here is a summary of some of that research: Reincarnation research
Secondly, the traditions that explicitly talk about reincarnation make it perfectly clear that the mechanism is not randomness, but causal responsibility. Your skillset, perspectives and circumstances are not random, but the very result of past-like actions(i.e. karma). If true, that points towards a continuum of identity across lives, not a series of disconnected episodes. The whole meaning of it disappears if you reduce rebirth to a mere change of scenery. The meaning being learning, and the evolution of consciousness through cause and effect explored through lessons experienced in ever-changing circumstances.