Yeah one of the main causes of the downfall of chariot warfare in the ancient world was that horses were bred that could carry a fully armed rider with armour for a long enough period of time.

Disclaimer: I know very little about anything.

I'm not so sure. There's plenty of accounts of ancient warriors using ridden horses as transportation. It probably has more to do with a chariot being more compatible with horse/soldier training and soldier gear at the time. Riding a horse into battle takes a lot of unique training and gear, and camels were the better option for a lot of the latitude around North Africa/Middle East, where you had ancient empires with the ability to research technology.

The idea that horses had to embiggen, I think, comes from the Persians. They wanted the world's first heavy cavalry and they certainly needed bigger horses for a fully armored rider. But light cavalry has evidence dating back to at least 5,000 B.C. thanks to the proto mongols. (Central Asian tribes before they were united)