Not to be overly contrarian, but ...
Planing is a terrible word for the phenomenon in question, which is when the flex characteristics of the bike are such that the energy stored in deformation (of the frame and all the attached parts) is efficiently returned to power the rear wheel during the lower power part of the pedaling cycle. When a boat planes, it rises out of the water, resulting in a large reduction in coefficient of drag. The equivalent on a bicycle would be the development of a vacuum around the bike and rider at a certain speed. That would be fun, but it's certainly not what's happening on earth. Ironically, there is a well-known and used term in Jan's back yard, for the exact phenomenon he is trying to describe. Rowers have long used the word "swing" to describe a shell and oars whose flex characteristics synchronize well with their strokes, allowing them to go faster for a given power output. Jan claims that bikes that "plane" magically increase a rider's power output, but the reality is that bikes that swing well waste less of the rider's power. A better way to put it might be that such a bike puts more of the rider's power to the back wheel.
The flex characteristics of the frame are important, of course, but the entire bicycle (and its rider) is a system of springs and in such a system the softer springs affect flex first, with the stiffer springs becoming more relevant as the forces increase. For most of us on this list, we don't spend a lot of time putting enough power into the pedals to get to the point where frame flexibility is significantly tested. At 57kg, I can tell you that I rarely put out that kind of power. I have a brevet bike made of .7/.4/.7 standard diameter tubing, and I can make that frame flex, but not for very long. That bike rides on 42mm tires at about 33 psi, and the tires are definitely the soft springs in that system.
I don't attribute aluminum, or stiffer frames in general, to an increased focus on cadence. Track cyclists have always been obsessed with cadence. With the introduction of multiple gear systems for road biking came the opportunity to develop notions of "ideal" cadence. Note that when Jan talks about frames "planing" for him, he almost always talks about it working for his preferred cadence. Stiff frames, in fact, reduce the importance of cadence, as they reduce the contribution of the frame to swing (for a given power input). For me, cadence is only important when going uphill or into a headwind. It is important because I need enough momentum in my feet to keep a steady speed. Without that momentum, I am repeatedly accelerating during the power phase and decelerating during the non-power phase. That is terribly inefficient. And that is why, as discussed in the recent thread on gearing, it is so important to have low gears in steep hills. Long before aluminum frames were a twinkle in Gary Klein's eyes, cyclists talked about "staying on top of a gear" when climbing. It meant to maintain a fast enough cadence that you were pedaling smoothly, maintaining a constant speed. Cyclists have also long talked about using smaller gears and a higher cadence to "work your heart, not your legs."
So, I also don't have _the_ answer to why some bikes seem/feel/are faster than others. Many of my best Strava times on climbing segments and my best 100km time are on my Heron prototype, which is a road frame but has the heavy rear stays from the touring frame. You can feel the weight of the stays (and the weight of the old SunTour freewheel) when you pick up the bike. Maybe it's just that I have so much invested in that bike that it inspires me to push a little harder. I tend to believe Jan's hypothesis that stiffness in the downtube and chainstays and flex in the top tube, relative to each other, help a bike swing in a way that returns energy to the rear wheel. Interestingly, old Reynolds tube sets were always spec'd that way, with thinner walls in the top tube than in the down tube. Somewhere along the way they switched to the Columbus standard, where top tube and down tube walls are the same. The Heron Road bikes have .1mm thinner top tube walls than down tube, and my prototype has extra heavy stays, so there you go.
Ted Durant
Milwaukee WI USA