Great Stirrup Controversy
en.wikipedia.org
en.wikipedia.org
Whether the resolution of this question lets us extrapolate a general principle of technological determinism, whereby an invention topples a global order in place for centuries, it's an interesting anecdote, but I don't think it's a strong foundation for a heuristic we could apply to say, a text editor, cell phone, or a lambda function for that matter. We could use any of these things as the beginning of a post-hoc narrative explanation for a perceived historical change, but causality is weak.
However, if you are really interested in how cavalry works and would like to reason about this question, I recommend former games developer James Kingsley who has some great videos on it. He can actually ride, so his videos are a more serious investigation instead of just the speculation of a talking head on a lark.
https://www.youtube.com/playlist?list=PLEdnpoTDGX7IcHAPCjTs5...
Short article about him: https://www.bbc.com/news/business-39851253
Since I learned to ride I became skeptical of the importance of the stirrup for combat. It's a balance aid, but it doesn't actually stop you going backwards. It's even possible to jump without stirrups although it requires more training. Possibly the main benefit is in balancing sideways and standing upwards, for archery.
I always find these hard to imagine when the cause is a basic technological development. Surely, someone would have eventually invented the stirrup, given ridable horses.
It’s easier to try to imagine a world with no horses, or where they were unsuitable for riding.
Perhaps, though the stirrup as we think of it shows up a lot later than horseriding does. Although the stirrup seems obvious at first glance, it requires a number of advances in saddles to support, or at least to take full advantage of them.
That said, as the article points out, you don't need stirrups to have cavalry, or even heavy cavalry.
The key word is eventually. The number of inventions that are blindingly obvious yet took millennia to appear boggles the mind. A nice example is swimming, where various strokes appeared incredibly late in otherwise "advanced" cultures and only in imitation of other "primitive" cultures.
This isn't obvious to me. I'm not saying it's wrong, but I'm not convinced that it's right either. Henry Turtledove's short stories The Road Not Taken and Herbig-Haro explore a future where aliens invade Earth with FTL drives, but only basic weaponry. It turns out that FTL drives are a relatively simple technology, but one we missed. Not expanding outward in space forced us to pursue more competitive development of other technologies on Earth, and when the aliens invade we quickly kill them and take their FTL drives, suddenly becoming the dominant species in our part of the universe. It's just fiction, of course, but I think us having missed some basic tech is an interesting possibility. It's only theoretically possible to show that we missed something in the past, not the present, since the discovery of something which should have been obvious in the past makes it no longer valid as evidence of our failure to have discovered obvious things in the present -- it's been discovered now. That being said, can we think of such examples? Things that don't have any obvious barriers, but which we still failed to invent for long stretches of time? The screw as a fastener seems like a potential candidate to me; the Archimedes' screw was used to move water and grain in ~300 BC, and nails have been around since prehistory, but screws as fasteners don't show up until the 1400s AD. You could argue that the widespread adoption of screws in the 1800s AD required certain machine tools for mass manufacture of screws with threading at regular increments, but this doesn't explain the 1700 year gap between invention of the screw and any use of hand-crafted screws as fasteners. There could also be gaps in our understanding of this history, of course, but that would be true to varying degrees for any proposed example.
Steam machines might be another, basic ones were already in use in ancient Greece but their development stalled for millennia.
If the stirrup had clearly been invented at a different time than the emergence of feudalism, then the hypothesis would not have been advanced in the first place.
I'm not sure, could we make do with chariots and chariot archers? Would civilisation develop as normal, but more slowly in rough terrain?