Watched the video.
1. This video is focused on stiffness (which he properly calls "modulus"). Implicit in his argument seems to be that higher modulus=better, although he complicates the issue by talking about "torsional rigidity" vs. "stiffness". I'm not convinced stiffness for stiffness's sake is something to be desired in bikes. I like some bikes that are very stiff and other bikes that are less stiff depending on what I'm using the bike for. Also, tires and other component choices play a huge role in perceived "stiffness".
2. I have no idea if his engineering approach here is sound. I've watched several of his videos and they're entertaining.
3. I believe the real world ride characteristics of a given frame have more to do with how that frame is designed and engineered than the lab-measured physical characteristics of the raw material. You can make floppy carbon bikes and too-stiff Ti bikes. Given that, I focus more on other frame material characteristics: cost, toughness, aesthetic possibilities, corrosion resistance etc. Carbon actually fares pretty well in this regard.

I currently own bikes made from all four primary frame materials. The frame material is only one factor behind why I chose each bike.