I've found I like using the chip that gives you invincibility after a perfect parry, it's nice for boss fights and being able to fight recklessly for a few beats after feels really satisfying.
It seems like the game is coded such that parries only interact with attacks that are about to hit you, and since you're invincible you're not able to parry an attack. It would be nice to be able to parry these attacks to build stun or score.
I've also encountered some strange interactions with invincibility and parry challenges for the same reason, a perfect parry leads to not being able to block the rest of it so you don't get the counter hit since you didn't technically do the challenge