I would have no problem to be able to adopt some of those orphan children in Ishgard but only if they either just stay in the house/with the scions or if they stay where they are but look a little better and we could interact a little with them. But we are adventurers and it would be quite dangerous to have a child that will follow us around.

Even if I find the idea quite cute I dont think that they ever would implement something like that. I mean the minions themselves barely have any real content behind them and are just there. So for it to even make some sense they would really need to put a lot of work into this. And I am not sure if its worth it in the end especially since we already get one dungeon less for extra content.

Before they put that much work/time into such a thing I would find it better if they give us the path companions back. At least those would have some use.