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.
Or do they just get tarred with 'Well, they work in finance, of course they are all crooks' brush?
There’s also a clear tolerance of securities fraud as long as you subscribe to certain ideologies — eg, NYSE allowing Disney to trade when they’re clearly stealing/destroying shareholder assets to advance the ideology of a cabal of executives and fiduciaries.
I'm not going to waste my time sifting through it to find evidence for a claim you're making.
Make a specific claim of corruption, and provide evidence for it.
Much easier to just go by gut feeling though isn't it.
What now? I'm sure you are going to say that they settled because they were innocent, right? And that they halted trades 'by mistake', not on a purpose