"You have simply replaced random outcomes with random causes which makes no practical difference."

It IS the VERY and critically important practical difference....

If your 'practical difference' claim simply means that you are confused and assume that 'random causation' "a" always produces 'random outcome' "A"... but in that case it is a one to one relationship, and so the idea that the outcome itself is 'random' (and unrelated to the input, irrespective of whether THAT is 'random' or not) is shot down....

But now if input "a" always produces a different output ('random' - 'non-deterministic') then we can learn nothing by studying it anyway ... unless the output displays a statistical output curve, in which case it is still consistently deterministic.... just that we can only assign a percentage certainty to the outcomes...

If you don't mean either of the above, I have no idea what you could mean....