Absolutely, but it's not just nonprofits. It's become a competitive barrier to entry exercise throughout industry. Only the big, established players can afford to do this, and it functions as a sort of tax.
“Tax” is a great model on which to view the situation! I also think of these leadership positions, critical race theory / anti-racism / unconscious bias trainings, and diversity initiatives as a sort of insurance policy against social media-driven outrage. A large organization pays the "premium" to prevent a possible large loss of brand reputation.
As you stated, this functions to benefit the large organizations that can afford the premiums while smaller organizations will go unprotected and pay the costs of the outrage that will be deflected their way.
I think it depends on how much attention the smaller organization gets. I can totally see a CDO being a de-facto requirement for Bay Area startups due to all the pressure from the politics in the area.
It's also possible a small to mid size organization gets into some imbroglio on Twitter and realizes they need a CDO to try and stop the bad PR.
