EVILADY ART

You will witness true horror

The thing is, in any RPG, the protagonist is often meant to be a bit of a blank slate, with room to implement one's own OC, personality, and headcanons. The fact that game dialogue can sometimes feel noncommittal, or the fact that the responses can vary so widely, speaks to this: you can be anyone, so you are not forced to be any one thing specifically.

But when you carry that OC with you, out of that game? The role of the protagonist in the narrative shifts: it is yours. It belongs not to everyone (which is how they build the game) but to you, to your iteration and interpretation of the game's events. The protagonist goes from being the vessel through which we experience the story to being the main character of a narrative.

When we write, then (though this is also true for non-writers with OCs!) the protagonist - be they Tav, Rook, the Inquisitor, the Rogue Trader, anything - benefits from having more detail, and especially more extravagant detail. They are (most often) the POV character of the narrative. They are the lens through which we, as readers in fandom, experience your story.

So yes: make them special.

Yes: make them unhinged.

Yes: make them go on whatever emotional journey you like.