Potential labor issues would be one part of it, although no umpire would need to lose his job over automated balls and strikes. I also have a theory - which admittedly borders on the crackpot - that there's a desire on MLB's part to retain an ability to manipulate the game to maintain some sort of idealized balance between offense and defense. Expanding and shrinking the strike zone as necessary would be an important tool in the toolbox. Don't expect me to defend this notion too vigorously, but we all know that the specter of league-wide anemic offense is one thing that keeps Manfred up at night.
Now that the technology is all but proven and there are websites dedicated to putting umpires under the microscope every single day, it's only a matter of time before the pressure to change becomes overwhelming IMO. I predict that it will take a playoff impacting mistake to provide the tipping point though.