> If the complexity of chess is finite this is possible.

This is like saying the distance to Mars is finite so it should be possible to just go and live there. It's not theoretically impossible, but at the time it is practically impossible. There are real engineering challenges between here and there that have not yet been solved and from the looks of it, it will be at least several more decades before we get there.

In your example, you gloss over the construction of a "finite time oracle" by just saying "just train it until it is perfect". If humanity knew how to do that we could solve a whole other (more interesting) set of problems, but we don't.