To extend your point, being able to "switch-pitch", that is, pitch with both your right and left arm, would be even more confusing to batters. And be able to throw from multiple arm angles with both arms!! Okay, enough sarcasm. Honestly, the reason is that most pitchers, biomechanically, have an arm slot that works for them to produce velocity, accuracy, and consistency. It is very common for pitchers to get to the major leagues with a certain arm slot, and have success, but for some reason either their pitching coach, or they themselves, will have the brilliant idea to change arm slots to "create more movement" or "hide the ball better", etc. Unfortunately, however, at least from several pitchers I have seen, it has done more harm than good.
Some examples of this off the top of my head are:
These are just a few examples to stir the pot, I am sure others will think of more, and also think of some examples who benefited tremendously from changing their arm slot. Consistency in mechanics & delivery is one of, if not the single most, important element in a successful pitcher. That being said, teaching a pitcher to change arm slots constantly can lead to inconsistency and injury. While it may work for some, my conclusion is that it will not work for the majority of pitchers.