Nonprofits have privacy too:

https://en.m.wikipedia.org/wiki/NAACP_v._Alabama

That said, there are a lot of operational advantages to being a for-profit corporation. Chan-Zuckerberg is organized this way. Other nonprofits try to have it both ways where the for-profit entity operates the business while being owned by a nonprofit. It has not worked out great for OpenAI. Patagonia converted to this model recently.