I have a theory that the fact that the net on its own is a decent player is precisely its greatest weakness. Obviously the deep NN must be doing some type of search, but this search is maybe slower than the engine search, because it can't interact with the various engine cache tables, and feed into the statistics used to heuristically order moves.

Stockfish NNUE is a much simpler neural net that's just a really strong, static evaluation function, not doing its own search and therefore the engine can search further and get the most out of the data(transposition table, continuation tables etc) generated by that search.

I think the AlphaGo architecture makes more sense for Go than the chess family of games, but that's a different discussion altogether.