I don't have a direct answer to your question, but just thinking about it leads me to a slippery slope. As network-sponsored prop bets generate revenue and become an integral part of the "MLB experience," how long will it be before players take note and try just a little harder to reach individual milestones, even if it's subconscious? If Eduardo Rodriguez knows that the over-under on strikeouts is 5.5, is it possible that he intentionally pitches away from contact when he's sitting on 5 strikeouts to see if he can hit the over, even if he doesn't have a direct financial interest?
When I see Big Papi flashing a suitcase full of cash and making predictions on the pre-game show, it's not hard to imagine a post-game interview where he says good-naturedly, "Come on, man, you made me look bad." I understand that these theoretical micro-influences already exist with sportsbooks, but I'd prefer a clear wall of separation between those sportsbooks and MLB partners with direct access to the managers and players.
Also, all of the finger-wagging about how Rose never tried to change his gambling ways rings hollow now. Granted, betting on baseball as an active participant is a cardinal sin, and Rose deserves his exile. But Giamatti, Selig, and Manfred went a step further with the proselytizing and suggested that Rose should re-examine his entire way of life. As Manfred put it, "Mr. Rose has not presented credible evidence of a reconfigured life either by an honest acceptance by him of his wrongdoing … or by a rigorous, self-aware and sustained program of avoidance by him of all the circumstances that led to his permanent ineligibility in 1989." Manfred also said that Rose's spiritual transformation "must begin with a complete rejection of the practices and habits that comprised his violations of Rule 21."
Manfred's implication is that someone so addicted to gambling that it infected his baseball life could only recover by avoiding the sinful activity entirely, even if it no longer implicates Rule 21. I'm offended that MLB is preaching total abstinence for Rose, while doing its best to usher in the next wave of gambling addicts.