It's important to have as direct and stiff a line of power transfer as possible, especially for a sprinter, where instant reaction is required.
I'm not trying to pile on, cyclespeed. But your comment points to something many people miss: you don't get more power or "faster response" from a stiffer shoe or even a stiffer frame.
Another vote for Bonts, the top-end power increase is uncanny, both in the power data and feel <snip>
I don't doubt that you *feel* a lot more powerful, but if you're generating more power with your Bonts, it's because you're pedaling harder when you wear them. (This sort of effect is almost impossible to avoid; that's why double-blind studies are the scientific gold standard).
Most power meter specs list an accuracy on the order of +/- 1.5 percent. Accuracy is not the same thing as precision, of course, but it's not unreasonable to assume that you'd need to make ~2% more power to get a clear increase in the reading from your power meter.
Let's say you sprint at 1200 watts for 10 seconds. So when you put on your Bonts, and pedal that hard, your meter now reads 24 watts higher (1224 W). That means your regular shoes were dissipating at least 12 watts each. That's a lot! It's not power that matters here, but energy. Energy is in units of Joules (for SI) and 1 Joule=1 Watt * 1 second. So in a ten-second sprint, we get a total energy of 120 Joules (10s * 12 W = 120 J).
Carbon composites have a specific heat capacity in the neighborhood of 1 J/g-°C. The carbon soles of a high-end road shoe weigh in the neighborhood of 100 grams each. But, treating the sole as a beam in bending, the vast majority of the strain (and therefore energy absorption) is happening over about 30% of that mass. Now we can apply the dissipated energy to the part of the sole that is actually flexing to calculate the temperature rise:
(120 Joules / 30 grams) * 1 J/g-°C = 4°C.
So the sole will heat up in the area right behind the cleat by 4°C (or 7.2°F). That's enough to feel.
Moreover, if temperature rises of 4°C were typical, one wouldn't need a thermal camera capable of distinguishing 0.02°C to study stress via imaging.
Now, I'm not discounting the importance of rider feel. Confidence is critical, and many people feel more confident knowing they've got a stiff frame or when they're wearing their special sprinting shoes. If you think you'll go faster, you often will—and that's the problem of trying to gauge these things by feel, even if a power meter is involved.
Once, when I was a junior, I was practicing sprints with my friend. He was usually a little better than me over 200m, so he was a great person to practice with. As I led out the first round, I clicked into my highest gear and gave it my all. I was expecting my friend to come around me and beat me to the line by half a bike length or so, but he didn't. When I crossed the line and looked back, I saw that I had ridden him right off my wheel. It was amazing!
Here's what happened: I believed I was riding with junior gearing, which at the time was limited to a 53/15 gear. But in fact I had put on the wheel I used for senior races, which gave me a 53/13 gear. My friend had the same gearing, but I was expecting to turn a 53/15 at about 125 RPM. I hit maybe 110 RPM in my 53/13 without realizing anything was amiss.
So yeah, confidence helps you make watts, no doubt. Stiffness, however, does not.