After watching Noxious' video, the main point that caught my attention is his central assumption that Wizards 'eventually wanted every deck to have a companion'. At first, this thesis seemed absolutely bizarre to me. If they wanted the mechanic to be accessible, wouldn't their first instinct be to not even bother with deckbuilding restrictions for them and start out at a much lower power level, like
Shivan Dragon power level?
After thinking a bit about it, the idea made more sense to me. It's very possible they actually started like outlined above, felt it didn't have enough of an impact on the game and ended up with the Companions we now have before us, and they balanced out fairly well in Standard playtests; however they broke Limited. In a desperate attempt to fix the format they included the restrictions they figured would probably applied to them; couldn't think of good ones for Lutri and Yorion and threw some random requirements onto them.
Seeing the companions in this light, what would happen to them?
-Yorion's deckbuilding restriction turned out to be the de facto easiest to meet in Standard, which is why he is seen so much and has little counterplay. On the other hand, the restriction essentially mechanic-banned it in EDH/Commander.
Also, him being a 3-for-1 isn't that bad at face value - Lurrus and Lutri are immediate 2-for-1s, Keruga is a fairly easy 3-for-1, Gyruda ca easily be as well. The most broken things about it are its interactions with Agent of Treachery and Elspeth Conquers Death, the former likely being banned anyways, the latter could
maybe be worked with?
-Lurrus, Obosh, Gyruda and Keruga, while you'd still want to build decently close to their restriction, suddenly do not exclude half of the cardpool (Lurrus in older formats still seems broken though)
-Lutri, instead of killing virtually any consistency a deck has, would actually be a strong Standard playable (good addition to Wilderness decks) as well as being a decent Companion in EDH/Brawl instead of being mechanic-banned.
-Umori would enjoy more flexibility; maybe EDH/Brawl would have to watch out for it
-Jegantha will not break Standard anytime soon (EDH/Brawl might have to watch out for it though)
-Kaheera is suddenly companion-able; still not too strong since you probably want to be close to its requirement anyway, but you can actually add Humans to the deck now
-Zirda is suddenly companion-able and a nice addition to aggressive decks (you'd have to watch out for the interaction with Winota and some older formats)
It feels weird to balance the mechanic this way, but it does make some sense to me.
In this case, I believe Agent of Treachery still has to go, and Fires/ECD/Winota would jump up in my ban ratings by quite a bit.