I would really like chess engines to build in some kind of "variance" or "sharpness" metric and display it alongside the actual advantage.

I'm not entirely sure what the metric would be, but some conceptual ratio of how many moves (over, say, the next 5 turns) throw away the advantage to less than +1 or even reverse it, vs how many moves maintain that advantage.

Obviously you would disable that calculation during competitive play (you don't want your engine wasting time summing up clearly losing moves that will never be played), but for live analysis it would be great to see, say... +8 advantage with 90% 'sharpness' ratio, meaning that a player needs to find the top 10% of candidate moves in the next 5 full moves in order to maintain that +8 advantage, or it will drop.

Or potentially you could even display a graph of this data, like an S shaped curve one showing if the bulk of calculated lines are displaying a huge advantage or just a very singular one.

Would be great for commentary.