Every bow-wielding culture in the world (which means most of the world) found suitable natural materials and constructions to make and use bows and arrows for feeding and defending their families. That’s the beauty of it.
Even if we restrict ourselves to wooden bows, there are literally tens of thousands of tree and shrub species that make excellent bows. I have used roughly 60 different woods myself. And no, bows out of yew wood aren’t anything special. They are only special within certain bowmaking traditions.
Modern people, especially engineers, are big on efficiency gains, but that misses the mark when it comes to feeding and defending your family. Simplicity, dependability and unobtrusiveness are key features here (and also forms of efficiency).
Shaping and bending to form four thin slats (as in the pic in the OP) of wood using simple tools, before even having a bow to shoot, is a lot of work for questionable gain. Lots of extra high-strength string needed, as well.
In general, bow-wielding cultures put lots of effort into their arrows, which are by far the most important component of the weapon system. The simplest bow with great arrows is infinitely deadlier than a super bow with so-so arrows.
Let’s try using the multi-limb bow while sneaking up on a deer in dense bushland. Those extra limbs with their extra strings will catch vegetation like a mother, creating lots of extra noise and motion that flags game. Even simple recurved ends on a bow tend to have this problem. The multi-limb bow multiplies it.
A silent shot cycle in itself is important as well, with low-velocity, short range projectile weapons such as natural material bows. I wonder what kind of noise the multi-limb bow makes on release? At least the main bow slapping against the closest extra limb must be noisy as hell. Slightly loud bows make deer jump the string, meaning they duck the arrow, spooked by the launch noise. A really loud bow alerts game across a mile, as well.
Native Americans of the West commonly carried their bows in bow quivers, attached to the arrow quivers, for easy, hands free transportation. No way to carry the multi-limb bow like that.
When Manhattan Project physicists (and keen archers) Klopsteg, Nagler & Hickman studied the bow and arrow in detail, they concluded:
“the adoption of a specific [bow] design was accompanied with a very good reason and science has only been able to make slight improvements.”
Of course, they had no way to know about the compound bows of the latter 20th century and beyond. But those have nothing to do with pre-modern times, materials or realities.