These examples are arguably qualitatively different from what's happening with Boeing's self-inspection.
I used to work at an organization that was governed by multiple of the SROs you list there. Here's how it worked: They set rules, we followed them, they monitored and audited us. There were also governmental organizations monitoring both them and us.
I think that the key distinction here is not actually public vs. private. It's more of a "sunlight is the best disinfectant" situation. The simple knowledge that you have some external agency that doesn't have moral hazard concerns to compromise its interests that is keeping an eye on you, and that you know is keeping an eye on you, does a lot to incentivize better behavior. Is it perfect? No, far from it. But, at least in the specific case of the financial industry, it's not clear to me that a 100% governmental regulatory system would actually fare any better. I think that the unstated major premise of such an idea is that the people in charge of the governmental regulators - elected officials - are uncompromisable ethical paragons. And if you believe that, I've got some hot penny stocks that I'd like to tell you about.