I'm probably a softy on this one, but hear me out.
How would you respond to a side-quest where a kid loses their parents and the Inquisitor has the option to "adopt" them? (And you can decline either coldly or put them into reliable hands) Then their relationship would depend completely on you along with all of it's negative and positive consequences. Then things get dangerous towards the late-game and you find a trustworthy caretaker to take them out of harm's way.
For the record, the kid wouldn't actually go with you on missions (cause why would you bring a child into a warzone?), but would stay at the keep. The kid could also potentially die.
This was unexpected.

I suppose it would depend on the personality of my protagonist at the time. There are different issues that can arise, especially when your character is focused on closing the Breach. Do you have enough time to be a parent? Is there an issue of clashing cultures, or is the child of the same race and background as the protagonist?
With my first Inquisitor, I wouldn't mind adopting a child. The Dalish adopted Aveline, so I guess it wouldn't be implausible to do the same. I've done it in other games, to varying extents; my Telvanni and Redoran did in Skyrim, and Joel pretty much adopted Ellie in The Last of Us. This seems a bit more complicated than those circumstances, of course.