I rather doubt it.

Historically there has been a back-and-forth with chess engines....

Early engines tried to really "smart", but consequently couldn't really analyze very deeply, as they spent a lot of time on each position. Newer engines mostly churn through really deep analysis, going many layers deep, but are making comparatively simplistic analyses.

I guess I am asking whether it's valid to criticize the AI for not answering questions that it wasn't asked.

For instance, it wasn't asked to evaluate the pawn structure and provide that analysis as an output, but it certainly could be programmed to do so.

"For instance, it wasn't asked to evaluate the pawn structure and provide that analysis as an output, but it certainly could be programmed to do so."

This quite misses the point. These programs do that as a matter of course, for individual positions. But choosing a move is the result of evaluating many millions of positions and comparing the scores through tree pruning. The program cannot tell you that it chose one move over another because the chosen move is generally better for the pawn structure than the move not chosen, because it doesn't have that information and cannot obtain it.

>This quite misses the point.

Or, maybe you missed mine.

It should be possible. E.g. I've seen people train a neural network or similar to classify images and then "run it backwards" to get e.g. the image that the network thinks is most "panda".

That doesn't tell you why it thinks one image is "more panda" than another.

"If so, could it be just as easily programmed to answer those questions as it evaluates moves?"

No. A chess playing program's move score is a value obtained from treewise comparisons of the static evaluations of millions and millions of positions.