A trendy misunderstanding has reared its head as to what the discipline of computing, indeed the logic of science, are all about. I blame Penrose, of course, but he is only the most recent promulgator of the recurring misunderstanding.
There are only a countable number of computable functions, so it’s no surprise a natural system picked at random will have non-computable functional features. Saying not all natural systems are computable is like saying not all poems are sonnets. Writing a program to model a significant aspect of a natural system is like writing a sonnet to express a significant aspect of human experience. It’s a voluntary limitation programmers and poets accept for the sake of their elective-effective art.
And both have their uses.