I wonder if you could creatively combine this model with search algorithms to advance the state of the art in computer chess? I wouldn't be surprised to see such a bot pop up on tcec in a couple years.
The thing is classical chess (unlike eg; go) is essentially "solved" when run on computers capable of extreme depth. Modern chess engines play essentially flawlessly.
We really have no way to know this. But I would be very surprised if modern chess engines didn't regularly blunder into losing (from the perspective of a hypothetical 32-piece tablebase) positions, and very very surprised if modern chess engines perfectly converted tablebase-winning positions.
We do know this, there are many positions (primarily sharp middle game one's) where SF/lc0 will significantly change their evaluation as they go deeper.
This problem gets better the more time they spend on one position but it's an inevitable consequence of the horizon effect and it's why (except for 8 pieces or less), chess is far from solved.