Just going down the list from top 5% MMR, for heroes that force you on a very narrow line.
Battlegrounds Heroes
Mutanus, and he's probably unplayable without the buddy
Millhouse somewhat encourages shenanigans on 4, until you are strong enough to get to 6, and you're just trying to force comps
AFK. Honestly people play AFK bad with the buddy, you shouldn't just be sitting on 3. You should be using the buddy as a huge tempo boost to let you level and convert into a real comp.
Overlord Saurfang is pretty much Mechs or bust, and he's grossly unplayable without the buddy
Aranna's buddy really wants you to play cycle comps, and she's unplayable without the buddy
Curator but the buddy is just doing what the hero power does anyways.
Guff is a pretty terribly designed buddy that never should have been what it is
Onyxia kind of wants you to just force avenge stuff, but she's a garbage can hero anyways
That's really it imo for very narrow buddies. The reality is the buddies are generally just increase tempo for doing what your hero is better at doing anyways. All removing buddies is going to do is lower the power level/tempo, people are going to power to 6 even more. It's going to be boring and annoying, and in a month everyone's going to hate it.