You are assuming that designers would be overly simplistic about their work. Planes don't use their wings for propulsion, so why would a designer try to make them flap? That action isn't solving the same problem, and any engineer would know that. Likewise, tires roll in response to propulsion, whereas galloping legs are providing power. Frankly, the pistons inside an engine ARE closer to a gallop than to a roll. (Well, maybe not in a Wankel rotary engine, but...)

Leonardo da Vinci, notable designer, and many other sophisticated people considered flapping wing aircraft. It’s easy to dismiss it as simplistic hundreds of years later once practical solutions already exist.

No, flapping wing aircraft simply are less efficent for size scales that can carry a person. That's why the larger a bird's wingspan, the less frequently they flap, such that condors, storks etc. are basically fixed wing gliders.

We in the artificial world do have our own local optima with quad copter drones. Flapping here would be more efficient. Consider seagulls that dive and change direction instantly, and can respond to gusts without missing a beat. We have nothing approaching that maneuverability. This is an active area of research.

What do you mean 'no'? It's an empirical fact that very talented designers considered flapping wing flying machines, before they had the information that we have now. They were not 'overly simplistic' except in deep hindsight.

We aren't done designing flying machines. Maybe it will turn out that when we have sophisticated enough control mechanisms and materials, flapping will turn out to be the way to go after all.

Of course natural evolution has found only local minima in the fitness landscape, but as a designer it's been running its algorithm a lot longer than humans have. Its local minima may well be better than ours, and so worth trying to imitate.

Refer to the grandparent post as to why large flapping machines are unlikely.

This thread is so weird.

I think a piston engine is just a different thing than a gallop.

A 1 cylinder engine works a lot better than a 1 legged gallop.

You seem to misunderstand what biomimicry even is. It’s about identifying root problems and seeing how nature has already solved the same problems we’re trying to solve. The whole concept of first principles is there. Remember when Speedo invented new swimsuits that led to swimmers breaking world records left and right? That was due to biomimicry. Because sharks are fast and shark skin is not smooth under the microscope but instead has lots of tiny protrusions that create micro-turbulence along the surface that leads to less overall drag. And then creating a similar material for swimsuits. That is biomimicry. Not making freaking airplane wings flap to achieve lift. But instead, discovering that the way a hummingbird sweeps it’s wings back and forth creates an area of lower pressure above the wing that virtually sucks the wing up. Interestingly enough airplane wings are shaped in such a way that the wind travels faster above the wing than below the wing, creating a similar pressure difference and achieving lift.

The human brain is the best pattern matcher in existence and we continue to learn from it. Think about that.