I don't agree that "If you can't beat your own game, it needs rebalanced". I think as long as its technically possible, its fine. I like games that challenge people. However, that does not warrant insane difficulty spikes or challenges requiring perfect input with nearly inhuman precision.
I do agree that the difficulty spike in here is insane.
Originally there was also supposed to be Dad and he'd have a bark sprite when the fakeout would happen. However this wouldn't help either. The fakeouts do add an additional challenge that the player simply isn't prepared for and on top of that the even smaller reaction window essentially makes it either:
A) RNG battle, where you hope you don't get fakeouts and can use your focus fully on reacting as fast as possible
B) Focusing on both. This requires great reflexes + self control to not automatically shoot when a fakeout happens.
It's possible. Some of us did it. But going from shooting everyone first try to spending hours on the last boss is quite bullshit.
Making the reaction window smaller would make this work. As you mentioned, predictable fakeouts would make this work. Maybe other solutions are there too.
So yeah, you're right. To make the game better and more proper, this'd either need balancing or reworking.
But game being easy until you face Doki, then you get your ass kicked for hours sounds funnier xD