>What did he get wrong? He's saying the rate of exponential change is increasing, which I think is true. Like, the doubling rate is getting shorter with time.

Even doubling, meaning a relatively small exponent of 2, quickly results in a graph with an effectively vertical rate of change and increasingly astronomical numbers. A higher exponent, like 10 or 1,000,000 or whatever, results in the same vertical line even more quickly, and an even higher exponent becomes vertical even more quickly, ad infinitum.

That is what exponential equations do - increasingly graph to vertical, ever more sharply with ever higher exponents. Even an exponent to the power of an exponent multiplies the powers together to provide a higher exponent. A "compounding" exponential equation can only do the same thing - increasingly graph vertical. It's not helpful.