To kata or not to kata

There's a longstanding debate about the importance of kata to karate practice.  I doubt I'll be providing the last word on this topic for anybody, but I wanted to put my two cents in.
As far as I can tell there are three distinct benefits to kata practice:

1. A place for hiding techniques.  That low block to the left?  It's actually a lethal groin strike, or an over the shoulder throw, or whatever.  Studying kata can help us learn lots of cool techniques.  Unfortunately, this is not my strong suit, personally.
2. A method of exercise.  Kata practice can be great for overall body strength and developing power in your footwork.
3. Meditation.  The concentration required to learn and remember kata, as opposed to soemone shadowboxing with random techniques, is a form of mental training.

In my style we do a lot of different kata, and we often do our kata in weird ways - like adding a back spin to every techniqe where there's a forward step.  I remember thinking that this was a silly and impractical way to train (I don't do a lot of spinning during kumite), but I did it anyway, motivated by an upcoming belt test.  To my surprise, my movement during jiyu kumite was pleasantly improved by all the turning and spinning.  I believe that I'd strengthened my legs in ways beneficial to fighting by practicing my kata, in ways that weren't being addressed by squats and deadlifts.
I can see the points of those who are anti-kata, but I worry about the practice of abandoning kata for a couple of reasons.  First, they might be losing out on some of the physical benefits I mentioned.   Second, I don't know how we can be sure that there aren't still valuable bunkai hidden in the kata we practice.  I'm quite sure, given my personal interests, that I'm not going to be the one to finally figure out the real application of the fifth step of Seienchin.  But if I can learn it properly and transmit it to my students or my kohai, maybe one of them will find a really useful bunkai for it. If we all gave up the parts we don't understand that potential future gain would also be lost.