I thought more about the effect of IV/price on the value of the butterfly spread. Correct me if I’m wrong.
We agree that the spread reaches its max value when the underlying is at the middle strike on expiration day. Then, I think the value of the spread depends on how IV would predict this to happen given the amount of time remaining.
When there is still quite some time before expiration day, an increasing IV actually makes the spread worth more if the underlying is still far away from the strike, because this high IV means there is greater likelihood that the far-away underlying can reach the strike by expiration day. On the other hand, a decreasing IV may not be so good in this situation because there are still many days before expiration and the low volatility implies that the underlying is not going to make big move, not likely to reach the middle strike.
Again, profitability depends on likelihood of reaching the middle strike as predicted by volatility.
Please note: This analysis holds true for every conceivable option position, and is not specific to the butterfly.