The trouble is: there is no deterministic algorithm that can do the things neural networks can do.

For many of these problems, I think it is likely that no deterministic algorithm can exist because the problems are fundamentally underspecified. E.g. a common task in computer vision is generating a 3D depth map from a 2D image. This is inverting a lossy projection, so any solution must be a least partially a hallucination.

I think we just have to accept this. It's a different type of algorithm, built out of statistics instead of logic, with different strengths and weaknesses compared to traditional software.

I feel the same way. Analogy: we’ve been geologists this whole time, building our dynamic and interesting mechanical planet.

Now, biology exists. It’s wet and messy and impossible to understand (we haven’t invented the microscope yet). That doesn’t mean biological study is not worth doing.