I have to believe that the reasons for friendly-fire bans are outweighed considerably by the potential to troll or just to be a dick to your own team for no reason.
Let's say I'm hovering Eve. I played her post-rework a bunch on the PBE, and I'm quite confident that I can carry with her. The only real reason I had for queueing up today was to get an Eve game in. Now, it would be one thing if the enemy team banned me out, or if I was out-picked. But if my own teammate bans me, especially if I'm high in the pick order, that's telling me that without any knowledge of who I am or what kind of player I can be, my teammate is unilaterally imposing a restriction on me. Not only that, but it's a restriction that they COULD have used to ban away an enemy champion.
But that's intentionally a contentious pick. Let's take a real example from me last week: I hovered Yorick, and my teammate banned him. Yorick isn't a heavily contested pick at the moment, and he's one of the lowest ban rates in the game. There's no good reason to ban Yorick for any reason other than to troll me. Could I pick a different top laner? Sure, but I don't WANT to. I learned Yorick, I enjoy playing Yorick, and I picked Yorick as one of my mains because I'm virtually guaranteed to be able to pick him since he's not popular. That's the champ I queued up to play, and since my own teammate randomly denied that from me, I dodged.
Banning your own teammate's pick has a very narrow legitimate application. On the other hand, it's a relatively popular method of trolling. Surely preventing such bans wouldn't significantly damage the use of the banning tool, right?