I am a novice and no triathlete by any stretch of the imagination, but I would have to disagree with your coach. When I do a 2bk as opposed to a light flutter I definitely feel an energy savings. I can't even imagine swimming long-distance with a flutter. That being said, I think it is important to listen to others' critiques of the TI method. Speaking for myself, it is easy to get defensive of the TI way and dismiss others' criticisms of it, but it is more helpful to try to understand what they are seeing. And I HAVE seen that same jerkiness in some TI swimmers and want to steer clear of that in my own stroke. From what I can tell I think it is caused by a pause at the end of the pull. Instead of keeping the recovering arm moving, it is "stuck" in the water for a moment, then there is a bit of a rush to recover and a lunge forward. Also I believe spearing too deep leads to jerkiness, more up-and-down movement rather than straight forward. Doing a 2bk just emphasizes these problems but doesn't necessarily cause them. There is more of an emphasis on a "wind-up" before the hand entry and it can become more of a lurch forward than a smooth spear.
As for breathing I would say whatever is comfortable for you is best. If every three is enough for you I would say stick with that, because no matter how sneaky your breath is, it will still be the tiniest bit of interruption to your stroke.
Just my 2 cents.