Ostensibly, those directing public companies are beholden to shareholders to create a valuable company.
Those directing private companies can do whatever they want, including extracting all the wealth for personal gain and leaving a husk.
If you study the history of what investing in a company via shares has historically meant, you'll find that it's only really in the last half century that the "appreciation game" came to the forefront. Dividends yields (or equivalent) were the evaluation criteria for these investments prior to our current era.
You speak about inflation and stock as if the cause/effect relationship is crystal clear and unidirectional, I wouldn't be so confident about that.
I don't think "you don't want to beat inflation?!?!?!" is a good faith interpretation of what I'm talking about higher up in the thread - which is rampant speculation for the publicly traded companies, and behavior tantamount to rug pulls in the case of private equity.
The boogeyman we have made out of private equity is pretty silly. It's not like being purchased by a publicly traded corporation is that much different, or even just a private buyer.