The chain gets to weed out errors by starting with cells that got through functionally unblemished courtesy functioning error correcting mechanisms. Each new cycle gets a fully functional error correction mechanism, and is fault tolerant to the theoretical point of repopulation from a small point of individuals.

An individual human body has error correcting mechanisms that do not benefit from being renewed every cycle- they deteriorate over time, Individuals suffer from problems larger systems don't - a few cancerous cells can poison the whole individual, but a few cancerous individuals are likely to die with few offspring, and their offspring are also more likely to die with few offspring. If an individual is left with only a few correctly functioning cells, they have no recourse for rebuilding themself.

Species get a constant influx of fresh water, as it were, and individuals have to make do with a set quantity.