Or maybe it is a problem with the structure that fosters an environment. What comes to my mind is the exceptional case of OpenAI, which started as a nonprofit. Sure, it "ended badly" because of the known drama, but my guess is that besides the money that was poured into it, it thrived because researchers had kind of an "emotional safety net," meaning that they wouldn't be pressured for results as much. Probably the reason some startups perform much better too.
I think career continuity matters, and you don't necessarily get that in the private sector for sure. This discontinuity then leads to practical work discontinuity, which means less work done (which is amplified by the non-decentralized nature of working in private compared to shared science in public, as you've explained).
My bottom line is that the private field could do better, and frankly it's kind of their loss. What I'm curious about is whether a "semi-private" approach is better: a non-profit or some kind of foundation. I guess in practice they're still private, but whether the money part can be "solved" through crowdfunding/some modern methods and whether they're viable long-term remains to be seen. One thing is for sure: a culture appreciative of science will definitely open more doors into novel methods of funding and organizing (maybe in the future these methods could rival the "traditional ways" of public science).