Noticing rolling doesn't require anything biological and the leap from that to wheel and axle is huge and not reflected in biological systems. People were making tools for 10s of thousands of years before they got around to wheels.
1) I suggest you look up the fascinating history of the wheel (as we know it so far)! The axel was actually more likely invented for turning wheels (think pottery); and again, humans are very capable of realizing that angular momentum is conserved when they spin (in that situation they are the axel).
2) I’m a little confused by your point. I concede that no organism has evolved to be Cart-like in its movements, but to say that it had no inspiration from biology seems to create a needlessly narrow definition of invention and inspiration.
3) I think the point you’re ultimately making is that people are clever beings and should use logic instead of simple observation. I think a better example there is nuclear physics (because it very strongly supports your point!)
But maybe, as usual, everyone is right/wrong. Contrary to your point, we are constantly finding new biological inspiration for invention (from nano to macro scale!), but to your point, some of the coolest stuff we do could never come out of the biological Monte Carlo simulation we are a part of.
1) No, a rolling thing is not a thing with an axle, no amount of looking things up will change that.
My overall point is that the bulk of human technology is not very strongly inspired by biological systems. We'd certainly like to build machines with some of the neat properties of organisms but until very recently we simply didn't have anything resembling the capability. Most machines are designed in principally different ways - modularity on a different scale, different use of materials to achieve reliability, etc. Wheel and axle is a just one of the most basic examples.
Wheel invented for pottery spinning. Pottery spinning machine very similar to human spinning. Probably inspired by human spinning
Human now has spinning machine. Human sees that when they spin down hill, they move easier. Human tips over pottery wheel.
Why is the above such a hard thing to believe? It’s supported by the archaeological record! You may not like that narrative but what’s the one you have?
And to be critical of the point youre making: there’s only so much chemistry and physics out there and ultimately we are made of biology, so what are you even saying? That we love making symmetrical objects but that has nothing to do with biological symmetry? That we forge metal because we are attracted to shiny things but that has nothing. To do with our obsession with looking at eyeballs? Maybe open your mind a bit?
But our current findings imply that the wheel and axel were invented for pottery turning and someone eventually got the cart thing going sometime after that.
Wait, you don’t think “humans ability to roll down a hill faster than they can walk” had anything to do with the wheel?
I don’t know about you, but I had an intuitive understanding of the wheel in kindergarten because that exact phenomenon.