A teammate got a pair of the reebok crossfit shoes...... they seemed stable and have less of a heel than oly shoes, but still too much of a heel for a wide powerlifting squat.
I've had good success having people squat in oly shoes, but only if they lack the flexibility to get down in a flat shoe, and never for powerlifting. On the platform I'll take my old school adidas or PF Flyers over the 5x more expensive oly shoes any day.
The OP has it exactly right though - any cushioning in the shoe becomes instability and lost force when lifting. With 1000+ on my back I can feel the difference between a platform made with rubber mats and a plywood platform, I couldn't imagine what the soft foam of a sneaker would feel like.....