I really think it would be cool if you could have a bighorner as a companionl. You could call it Babe as a reference to Paul Bunyan's blue ox. I know what your thinking but here me out. This companion may not necessarily be a combat heavy companion. ranged attacks are out of the question of course be maybe he could do some ram attacks or trample smaller enemies. The big draw to a bighorner companion is it should have a much larger carry capacity in contrast to the combat oriented characters, I'm talking like 400, 450, or 500 pounds carry capacity. Maybe babe would be more passive than other enemies and only attack when it was attacked. or maybe its a BATTLEHORNER and it s got armor plates on it and extra spikes on its helmet for ramming with. Or even better a companion that you can ride, you can shoot from the saddle and when you run full speed into an enemy it deals damage, or it could be more passive without armor and moves faster. that could be its companion quest perks. on way is to make it run faster or carry more weight and the other way is to give it battlehorn armor and make it better at dealing Damage.
I also think there should be companions who allow you to bypass skill checks or buff your skill like a smooth talker companion can interupt a conversation and win a speech check for you or he just gives you a boost to speech like + 20 or something. Or having a scientist who can hack computers or pass medicine checks for you. It makes sense to me.