I was thinking if we can have pets at our house then why not companions? The companions could stay home but then when you need them in a battle they would just pop up, and you could still use the companion management if you wanted to. I think it's a good idea what are you guys and girls.
I am not sure why you would want to have Companions in our houses.
For each Companion that is in our house, a space for that house (inside or outside) would be taken up.
When Pets are released into our houses, each one takes up one space and we can no longer train or use that Pet till we reequip it. I think that Companions would be treated similarly since we would not have ready access to them. This would mean they would not just "pop up" in battle if we need them like they do now. Also, any Companions in a house could not go out on orders.
I've thought of this before, too! Maybe when you put them in your house, they are listed as "busy" on your companion list. If you press "Belay Order" (which might say something different when they are placed, like "Recall" or "Summon") they will be picked up out of your house and ready for combat.