MLB already had a third party game to "reach more people", but, they found out making great games is hard, and their game was not even in the same ballpark (see what I did there) in quality to the years of pedigree. I am more than willing to bet (chirp chirp) they approached Sony when it was time for licensing renewal (which it was, I can't remember how long they sign them for but I want to say in the 7 to 10 years range) after their own 3rd party failures, with a sweetheart deal for the MLB 3rd party license, since it's already a well established revenue machine and a huge risk to get another developer to try and make a game, a good sim baseball game at that, year 1.
I know some baby nuts want to paint the picture that the MLB was going to "yank the first party license or else" to the most popular baseball game out there, which makes the majority (like literally 99%) of their video game licensing revenue, and give it to some company that has no game in the wings, and take the risk of not losing any revenue at all without any proven products. That is as delusional as it gets. Said companies (EA/2K) could have had the license all along, but I bet nobody was biting. The Show is a powerhouse, and it would take years of a pricey investment to build a competent competitive product. 2K found out the hard way.
It was mutually agreed on, and more than likely MLB was like, "now hear us out, DD is growing ten fold year over year, we could not get our own game off the ground, this shit is tough, we agree, so let's get that MUT/FUT like expansive monies! Don't worry about other platform distribution, we will handle all of the publishing logistics for you, just churn out the well established quality product as you have always done, have the 3rd party license on lock, and let's explode together."
But keep fooling yourselves that they were going to "destroy their numero uno gaming money machine", OR ELSE!