I could be wrong, but I think the stiffness a racer is after is out of plane bending stiffness "below the lines". One "line" being the line between the bottom of the head tube and the rear axle. The other "line" is from the head tube to the front axle. These are the the portions of the frame which would flex under load and tend to sap energy.

It is also important to have some in plane compliance, to soften the ride.

You'd also want a low hysteresis material so it will spring back after flexing. I would also bet hysteresis can be adversely affected by poor workmanship.

If the seat tube flexes a little, I'm not sure it matters in terms of energy transmission.

I don't think so. I think it is still limited by the modulus of the material (modulus of elasticity).