Great analysis! I wonder whether you can also incorporate puzzle usage in this.

"But while I have the data here, let's take a moment to answer the question everyone's asking: does playing more games make you a better chess player?

Intuitively, the answer seems like it should be yes. Seems like experience should be a huge factor in someone's chess strength. It also seems like the go-to answer many of the top players recommend for improving at chess."

That's actually not what I've seen top trainers recommend, at least for improvement at classical time controls. They recommend playing something like one or two games a day but carefully analyzing each game afterwards.