I ran a bunch of sims on 3CP once. I wasn't able to calculate the exact EV of knowing peoples' cards, but I was able to calculate the EV of not knowing ANYONE'S (besides your own) cards and the EV of knowing the dealer's cards directly. To gauge how much of that EV you can gain from partial knowledge, I then calculated the percentage advantage of guessing the dealer's cards based on other's cards. Bottom line: the dealer has a huge number of 3-card combinations, whether it's out of 50 (53 - your 3) or out of 32 (53 - 7*3), and the percentage I calculated was small.
There are a few obvious plays - obviously, if all the aces and kings are in player hands, you play just about anything because the probability of dealer qualifying is really low. But those scenarios come up rarely enough that you can't overcome the house edge on your base bet.
Playing the "pairs or better" bet is even worse - now your spread essentially drops to 3:2 rather than 2:1.