>>1609203Stiffness is generally wanted in certain directions such as at the chainstays for efficient power transfer to the rear wheel and the bottom bracket, and also at the headtube and fork for predictable handling and a good ride feel, and for resisting flexing due to braking forces. In general if your bottom bracket area is relatively flexy, as it can be on thin-tubed steel bikes, the bike can feel sort of dampened when putting down pedalling force. That's why newer bikes (allow and carbon) tend to have wider bottom brackets and thicker chainstays to maximise that feeling of connection to the road as you push.
The opposite is true for chainstays, seattube and handlebars to an extent - if you can build in vertical compliance (the ability to flex in a up and down axis) without adding too much flex rotationally or laterally, you can make the bike absorb some of the road buzz and vibration while still feeling fast and stiff. Lots of bikes have ways of building this into the seattube, as you can isolate most of the rider from the vibrations of the frame while still keeping their legs engaged with the stiff parts of the frame. It can be as simple as having more seattube exposed which makes a longer tube which is more flexy (like a Giant TCR), or building specific mechanisms to absorb vibrations at the seat tube junction (like on Trek road bikes and the newest Canyons aeroad).
It's actually sort of a myth that a flexy bike absorbs your energy, as it acts like a spring and most of that energy is pushed back into the road somehow. Only a very small percentage is lost as friction as the frame flexes. It's just it feels less responsive and sort of smooths out the ride feel. This is often a good thing on a endurance or commuter bike where you want a nice smooth ride but on race bikes they're trying to make it feel very fast in its response to your pedalling and that usually means stiffening up the areas around the power transfer.