Unfortunately, what might come of this is that MLB will be forced to rig up additional protective netting around the ballpark, making it tougher to see the game from the good seats. I'm old enough to remember when the netting behind home plate was minimal - you really had to pay attention then and many people actually brought gloves to games. Not to collect a souvenir or to get it autographed - but to protect themselves!
Well, you are right about the baseball team winning these cases. I thought the fact that it was a broken bat and not a ball could make a difference, but this nice little white paper on the topic (baseball and hockey) spells out the recent history quite nicely.
https://www.law.du.edu/documents/sports-and-entertainment-law-journal/issues/05/05-Augustine.pdf
Remember, the NHL had to put in netting around the ends of the rink after a fan was killed by the impact of a hockey puck at a Columbus Blue Jackets home game in 2002.
I have my doubts about how well that indemnity statement would hold up in court.