I don't think philosophizing about it serves much purpose. Just imagine applying that thinking to the mouse pointer on your PC - "it's ok that the pointer lags behind where my hand is moving by 200-400ms, because it, as a character, should have its own agency, and I'm just directing it!", lol.The internal thought path argument depends on if the viewpoint is whether you ARE Arthur vs you DIRECTING Arthur's story. It's clear the devs had discretion whether to make it 200ms (potential engine limit) or 400ms (actual animation).
In the end, whatever the intent or limitations are, the person interacting with the game end up waiting for things to happen that they shouldn't need to wait on. Also, what you are saying is clear, is not actually clear at all. Yeah, the input lag due to rendering process may be 200ms but that doesn't mean that animation could start that quickly if they wanted, because the animation engine could easily be adding extra lag.