BH will outperform only Constant mix in trending market and outperform CPPI in non-trending market thus is always in the middle.
Well, market is down during one trend and reverse in another trend. Never is constantly in down trend. BH may be optimal strategy to avoid high transactions costs caused by frequent rebalancing.
Relative to Constant Mix, Buy and Hold outperforms in a down-trending market because Constant Mix buys back to target on the way down, accumulating a larger position of declining asset values increasing the loss vs Buy and Hold while the trend continues.