I think there is often a lack of distinction between situations where uncertainty is due randomness in the natural process, versus situations where uncertainty is due to your incomplete state of knowledge.

For example, a coin flip is physically deterministic but you can't take advantage of that in a normal coin flip situation. But if you have a chunk of radioactive material and two particle detectors held nearby, I don't know of any way even theoretically to determine which will trigger first -- that would be physically nondeterministic (unless I'm wrong, but other situation could be i.e. famously quantum experiments).

Then, most of the situation that are physically nondeterministic are things that we experience is a way that is aggregated over a large number of events: i.e. you aren't seeing individual particle emissions, you are just eventually getting radiation poisoning. It takes special equipment to experience the probabilistic nature of nuclear radiation, brownian motion, etc.

So there are really lots of natural processess that are probabilistic but you only experience them in aggregate which conceals it, but then you have incomplete knowledge about the world which re-introduces the uncertainty.