This is something I've been looking into, so I can provide a few thoughts:
1) I think a lot of whether a protection bet is optimal has to do with his intentions with the hand we mean to fold out. The two extremes being that either never bluffs or always bluffs.
2) If he bluffs always with the hand, assuming we can make a profitable call vs his range, then it becomes a clear check for us on the turn.
3) If he never bluffs, he essentially freerolls us with his equity and we stand to lose actually more than his equity share in the pot due to implied odds. If we cannot call anyway, it still sucks to get freerolled like that, even for a small percentage of the pot. If he bluffs balancedly with the hand we mean to protect against, that's the worst of all.
4) So in light of all that it seems like we should bet for protection more often in spots where his folding range gets a lot of implied odds or bluffing equity on subsequent streets. This would make it clear that protection is much more valuable preflop and on the flop than on the turn.
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