I would dislike having strong AI provide any estimation about an ongoing game (whether it be score, territory, or even just win probability) to the players of the game.
If the score estimator were to be improved with strong AI, I would hope that the players of the game would not be able to access it (during the game), or that the feature would only be present for unranked games.
I made the following argument in another thread:
On another note, I actually hope that the “ongoing game score estimator” (I only mean the one that is available to players while the game is still ongoing, since using AI as tool to help in stone status and scoring disputes is different and potentially helpful) is not improved with strong AI. Right now, the score estimator is terrible, so I don’t think too many people take it seriously and it doesn’t impact too many games. However, if players had the ability to query a strong AI to evaluate the current position, then I think that would be a form of assistance that should not be allowed.
For example, sometimes my opponent would make a blunder that I would not realize and fail to capitalize on (essentially one blunder followed by another). However, with a strong AI giving score (or even just win probability) estimates, that might tip me off that my opponent’s last move presents an opportunity that I should search for, and thus a decent score estimator could provide unfair AI assistance.