> exponential

You keep using that word but are not understanding what it means. The further back you go on an exponential curve, the shallower it gets. Technological advancements are exponential. That's why they're faster now and slower way back when.

But that's also a simplification, because "humanity" is not a single entity with a single development curve. Civilizations grow and advance and then develop new technology and societal complexity faster and faster, and then they stagnate/fall, new ones evolve and branch off of them, etc.

Also there are major differences in society and technology between 5000 years ago and 1000 years ago, so I don't even understand your premise.

Lastly, why would riding animals need to be something a culture developed early? Animals are far more useful as food, wool, beasts of burden, etc. It also requires pretty sophisticated techniques and technology to effectively ride animals, especially on battle (stirrups for one thing). Hitching a cart, which were human powered before, to an animal is actually less complicated than developing horseback riding.