This would be super simple. We have 2 classifications, and literal millions of pitches to throw into a classifier. A neural net could perfectly simulate the amalgamation of all the umpire calls and hence could carry on in the future perfectly replicating the calls for what should and shouldn't be a checked swing .
And the bonus is we don't even care what those factors were since even the umps don't seem to know or agree. It will likely find whatever factors the umpires are subconsciously latching on to - who knows the umps might even be calling their checked swing calls based on if it is a sunny or cloudy day - they themselves can't tell us why they do it. If they can tell us, then it becomes easier again as we can program the criteria. We could even make different robo-umps that umpire like the different types of human umps.
And we could even throw in some random "humanness" (error) if that is what the fans want.
All this is easily solvable. There is no upside to human umpires apart from our affinity with fellow meatbags.
Would a robo-ump have "solved" all the problems - depends on what we consider solved. But we can say a robo ump will be cheaper, faster, and will be no worse if we program it that way. It can also be better if we can agree on the definition of better.