Another point of view on why it is not striking that we can model heat conduction well. The heat equation is well-posed, which among other things, means that the solution depends continuously of the input data. And we observe this in many physical systems, that small changes in the cause produces small changes in the effect, therefore, we should expect from good mathematical models of reality to display this property.

Now, orbital mechanics do display unstable behaviour. I don't dare to adventure on how people work around this. https://en.wikipedia.org/wiki/Well-posed_problem