While this is very fun as a mathematical exercise, it's completely irrelevant as a real tool for getting a better understanding of unknown processes in the real world.

The law only applies for certain types of processes, and is completely wrong for other types (e.g. a human who has lived 50 years may live 50 more, but one who has lived 100 years will certainly not live 100 more). So the question becomes: what type of process are you looking at? And that turns out to be exactly the question you started with: is there a fundamental limit to this growth curve, or not.

> The law only applies for certain types of processes

Did you even read the post? It’s an estimate in the context where you have zero information on which to base an accurate estimate. The author’s point is that if you’re making a different estimate you need to actually say what information is informing that.

Human lifespan is obviously not a case where we have zero information, so what is your point in bringing that up?