Just reading this thread and I too have been playing with the 2bk. A few thoughts:
1. One workout I swam two miles and just let my legs sorta dangle--forgot about them per some good advice here--and they fell into a 2bk kind of naturally. That's what got me onto the real trail of the 2bk. Also, without trying, you can begin to feel your hip rotation if you just forget about kicking. Worth a shot to just see how you feel. As others mentioned, I think a flutter kick helps to hide a multitude of sins.
2. I'm surprised that a triathlon coach would not be more of an advocate of preserving your legs for the bike and run. A 2bk really saves your legs I think. Yeah, you may go a bit slower but it's generally the fastest bike/run people that do best on tri's, right?
3. If you swim with a wetsuit your kick pretty much doesn't exist. So learning to work more w/ your core and a low key 2bk may translate better to open water swims?
4. Swimming every third breath means bilateral breathing. I think over time it's much better for your neck to breath from both sides.
I'm about two months into TI and am finding that while times are slower (slowly getting back to where I was--I think I bottomed out) I am more energized vs. drained when I get out of the pool. I also live up 25 steps and where I used to feel my legs heading up those steps after a swim I never do now (see 2bk point #2!)