I think such a design would be quite aesthetically unpleasing. Imagine a large grid of holes, each with some sort of rubber gasket. There wouldn’t be much wood to appreciate.
Each hole would have to be at least slightly larger than the marble, and then there would have to be adequate spacing between each hole in order for there to be enough material that it remains structurally sound. Taken altogether, that means that there would probably be more spacing between each marble than a simpler divot design, with enough spacing just to pick up the marbles.
For making divots, you mentioned simply drilling holes. I think cutting out spherical divots sized to fit the marbles would be more elegant.
Overall, I like the idea of considering novel go stone/board designs. It’s surprising and disappointing that despite the fact that go is an incredibly abstract game, set designs are dominated by the traditional aesthetic with virtually no alternatives available on the market.