^
I've not built one, but
AFAIK the purpose of the split cane construction goes beyond flexibility. It enables the builder to make a more flexible tube than a simple piece of bamboo, sure, but it also makes it possible to vary the flex, and to make a more durable structure compared to a single piece of bamboo by using only the strongest part of the bamboo. Much of the flex characteristics of bamboo flyrods are due to the resulting tubing diameter and the machining/tapering of the individual bamboo "wedge" sections. The thick "butt" end of a heavier weight fly rod can be very stiff and strong. Even a steel or carbon bike with the tubing diameter of a flyrod would be a noodle!
The species of bamboo used is also a major factor. Fly rod builders (as Peterpan1 pointed out) use what they call "tonkin cane" (I forget the botanical name). Other species may be more suitable for bikes, just as different species of wood are particularly suited to specific uses. (Hmm...yew forks and seatstays, anyone?)
My thought is that using the same techniques with the appropriate bamboo species on much wider diameter (compared to fishing rods) bike tubing would enhance strength, make a lighter tube, and enable fine tuning of frame stiffness; it should be possible to build a reasonably stiff, light, and responsive frame; perhaps in the league of a high quality steel frame.
This all might be academic, of course, if the labor intensive nature of split cane construction makes all this super costly.
(EDIT): If I knew how to do split cane construction, I would be trying it instead of speculating about it! Perhaps someone with the skills, equipment and inclination will be inspired to do so. Peterpan1, are you reading this?