The example he cites has a ball head. And carbon fiber bike frames are harsher than aluminum or steel because they are stiffer and transmit bumps straight to the rider without absorbing them. Steel flexes more than either, giving a more comfortable ride.
The frame part of a bicycle frame - the double diamond triangulated part - doesn't flex up-down to a degree that a rider could perceive, regardless of material. It is incredibly strong and stiff in the plane of the frame, because it is triangulated, like a bridge truss. (Less so sideways, but you don't sit on a bike sideways.) Flex occurs in the un-braced areas - the fork legs, the fork steerer, the seatpost, the handlebars. Of course, more vibration dampening is done by the soft parts such as the tire+tube, the seat, even the handlebar tape. This is a topic of much internet discussion/flaming, but a serious engineering analysis will show that even a steel bike diamond frame is so rigid that it doesn't damp out vibration compared to the other parts of the system.
What does this have to do with tripods (I'm trying to keep it relevant)? Well, for tripods we have the option of making the camera support much more massive than the camera (vs bicycles where a bike more massive than the rider is unappealing). We also have to consider braced vs unbraced parts of the structure, and any soft parts that could helpfully reduce vibration without compromising rigidity.
Clearly, extending the center column is a no-no, however with a big shaky camera, even the sturdiness of the center column clamp may have an effect. The height of the head above the tripod platform should be kept small, but the rigidity/inertia of the head is very important. I think many people use a ball or pan head that's undersized. Large solid ball heads exist but are typically expensive. Back on the first page of this thread, I suggested replacing the OP's smallish ball head with a pan head like a Bogen/Manfrotto 3047, which is heavy, unfashionable, but very sturdy.
For damping high frequency vibration, both the mass of the system, and any soft parts - such as the rubber/cork/plastic pads between camera and head, and head and tripod - should be relevant. Actually measuring vibration dampening is something that the author at thecentercolumn.net has ventured into:
https://thecentercolumn.com/2018/04/06/top-plate-stability/ and
https://thecentercolumn.com/2018/06/05/carbon-fiber-vs-aluminum-tripods/ for example. However, the simple but heavy answer is often "use a bigger support."