If a companion is down and you have a potion, on your turn it feels like you should be able to feed your companion a potion. I don't know if that's a house rule or a real rule for D&D 5e, but I've always played you can force-feed your companions potions if they're down.
Yes, when it first happened I was genuinely confused as to how to heal them. In that case they simply stood up and joined me when I healed at one of the nautiloid's healing-pod-things.
I agree, this is something which should be implemented, if only because it will give them back more HP than just the 1 from "Help". It should be a full action, though - not a bonus like it is for drinking it yourself.
I think the "Help" action is a fair tradeoff here. In 5e, stabilizing a companion would not pop them up with 1hp. They would be asleep at 0hp for a number of hours.