I'm sure there is a reason. I'm guessing it's banned by the rules. But I don't see where in the rules that this is banned. Will be great if anyone can enlighten me.

Rules I checked: https://pastebin.com/VtzvMpyW

Example speed run (P5 NMG #1):

The inventory scream skip:

For example, Soul Tyrant's scream wasn't skipped in the above speed run. However I just tried on my xbox that the inventory skip can be done with my dumb hands and get in at least one hit, so I imagine multiple hits in the hands of a top speed runner.