Yeah, I think something like that is going to happen sooner or later. Or maybe there would just be a number for "complexity level", since there doesn't have to be a plus or minus for it.
More importantly practically-speaking I think would be - you know how during the opening there are three bars for white, black and grey in the centre for the amount of draws in the database from that position? I feel like computers could and should also be able to come up with a computation for this bar themselves for during play. The reason this is so important is that there is no point being +0.1 for the whole game as white and then it gradually turning into a draw. Computers like this because they see any risk as losing some tiny advantage, but sometimes risk is necessary in order to win.
Sometimes one player is in a must-win position, and might sacrifice some advantage to make the game more double-edged, and it would be useful if the computer were able to calculate whether that makes sense. Think about also how we're trying to make a computer play chess as best we can make it play - but to play chess optimally you must sometimes play for a win while the opponent plays for a draw. Computers have never really had that to my knowledge, maybe they can be programmed to be more aggressive but to do that in the best way they would need to be able to calculate this tradeoff of increasing winning chances vs loss of objective advantage. Even just in the case of white vs black white should generally be playing for a win, and I believe many computers score higher if they are forced to play riskier openings in computer vs computer competition, though if that's not correct someone might be able to correct me on it.
Another interesting thing I've noticed is that oddly enough sometimes a weaker computer can show the complexity in a situation - by fluctuating itself near the start of the evaluation, so that tells you it's really complex. The modern superpowered computers seem to just arrive almost immediately at it nearly all the time. Also think about how if you had a "perfect" eval bar (game solved), everything goes to nil until there is a forced win at which point everything goes to +1 or -1, which is not useful for humans. This kind of happened in Caruana vs Nepo yesterday where the eval bar was either showing a win, or otherwise it would flip back to draw, it barely showed any in between. And this was barely comprehensible even with the lines of the computer why it would be a forced draw or win. At that point going by the computer evaluation can be a bit silly as it's humans that are playing the position.
So in summary we would like three things 1) Complexity/double-edgeness of position 2) winning vs drawing chances for each colour (somewhat related to the first one) and 3) number for the projected human advantage, even if a computer calculates it to the end as a forced win or draw dozens of moves later.
Right now we have the eval bar to evaluate the games while watching them but this feels like it greatly simplifies a highly complex game. It would be really cool if there was another eval bar that measured position complexity. It would give the commentators more to talk about since the eval bar basically provides us a way to determine who is winning WITH perfect play. However, this isn't completely realistic given that humans aren't in fact perfect.
I've thought about this a lot but especially when i was watching the Nepo v Caruana game today. The eval bar kept dramatically changing from equal to white was clearly winning several times throughout the second half of the game. The commentators said caruana had thrown the game because he missed a move and the eval bar dropped from totally winning to totally drawn. but in just a few moves the eval bar shot back up to white was clearly winning. The commentators were great, not trying to take away how good they were today, but the eval bar gives a very unrealistic representation of how GOOD these players are.
There's a lot you could do with a complexity eval bar too i think. You might be able to say that a certain move or series of moves represents a 2800 elo, so basically if one of these GMs find it it would make it so much more exciting. With this we could also see how the time impacts each of these complexities in the game. Anyways, was curious what the rest of the chess world thought. Let me know!