Let me rebutt a few of these statements, just for clarity. I believe there is a lot of incorrect concepts and incorrect statements in this thread, so I think a little clarity of thought is in order.
Originally Posted by
bbattle
It is understood that the triangles would be made of the same material, differing only in the lengths of their sides. This also means the angles of the triangles would be the same.
"Why are compact frames stiffer?" - By having smaller triangles, all other variables being equal, the frame is stiffer.
I don't think it is a good a-priori assumption. Large frame versus small frames, new designs versus older designs, etc. There are too many variables to just assume everyone understands this as a precondition. It is not unheard of for larger frames to be made of different tubing than a smaller frame of the same make/maker. Now, if you explicitly state this as a basis for your argument, then I have to agree.
Originally Posted by
bbattle
Professional racers and those who aspire to be like a pro racer. People who can appreciate a bike with a quick, responsive feel. That's not the majority of bicycle riders but it is why a great deal of research time and money is spent on designing new frames and frame materials.
There are many racers who intentionally introduce flex into their frames in order to improve their performance. Part of that "responsive feel" you mention is low hysteresis spring back.
I seem to recall the Paris-Roubaix (?) racers all wanted a more flexible frame because a significant portion of the race was over cobble stones and other poor road surfaces. A super-stiff frame was hard to control and beat the racer to death. Mountain bikers also introduce LOTS of compliance into their frames (front and rear suspension) for the same reason.
I think we all know we want a little compliance in between that front wheel and our hands, too. The fork stiffness, handlebar padding and gel inserts in our gloves is how we get it.
I'm not sure the OP was restricting the question to just racers, either. What about a touring bicycle?