Well, the thing is, our hand falls into a middling range of hands that aren't strong enough to raise for value happily but too strong to fold, thus we call. If our hand were stronger or weaker, we would be more inclined to raise for value or as a bluff respectively. Now bluffing would imply that we are trying to get the villain off a stronger hand, in which case, on this board, villain is very unlikely to fold a better hand, and therefore, we should be less inclined to bluff. This would make calling a more optimal play.

You mentioned that there would be many scare cards left in the deck, but wouldn't that make it better to call since villain would likely bluff more often?