Both of these are absolute rules that, in my opinion, shouldn’t be absolute.
I know the reason people give for standing on the throwing arm side of the rubber is to create angle in the trajectory of the pitch. My personal opinion is the increase in angle from moving to the throwing arm side of the rubber versus not doing so is really insignificant.
There is a good reason to stand on the glove arm side of the rubber. If you tend to stride to the throwing arm side and end up throwing back across your body, moving to the glove arm side can reduce how much you throw back across your body but reducing the “corner” you have to turn to get squared up to the target. This can also reduce or eliminate posture changes that can accompany one’s attempt to turn that corner. Of course, if you don’t have this issue, then this strategy is unnecessary.