But checking on a politician is an investment in your community with little personal return to yourself. It requires trust to think it will pay off to you.

Mancur Olson modelled it perfectly in The Logic Of Collective Action. 1000 people put 100 $1 bills or coins into a hat making it $100K and then someone steals $1000 out of it. What is more beneficial for you, to catch the thief and then you personally get your $1 back, or you, too, steal $1000 out of it? Setting morals aside, in the short run the second is better. The first one depends on the vague notion that if you let others fuck up the moral standards of your community, it cannot be beneficial for you in the long run. But this long run already requires trust. It already requires the belief the thief is an exception and not the norm: this is what is called trust. If you believe they all are thieves, low trust, your most efficient move is to steal too.

The mechanism can exist only a high-trust community where people think it is beneficial for them to prevent others for screwing up the common trust and moral standards. Once the standards and the trust both gets low, there can be no such mechanism.

The hat with the money is a good example because it shows how it easily becomes a death spiral, a race to the bottom, every single person you see stealing $1000 from the hate lowers the utility for you to chase them and raises the utility for you to do the same. There is a vicious circle, but no similar virtuous circle to bootstrap out of.

And I think my bootstap of fake trust is more like, if we really believe the other one will not steal from the hat, we feel less pressure for ourselves to do. The mechanism itself requires the trust that it is not the norm.

Again the model is this. If you are the first one to steal from the hat, the benefit is low - you don't need that stolen money in a functional society, you can also earn it, and the cost is high: people will go after you. If you are the 20th one to steal from the hat, the benefit is high: you need a buffer of savings, actually earning money in a society like that is hard, and the cost low: why exactly would they go after you.

Fake trust is the noble lie telling people "you would be the first one to steal from the hat". Get it?

BTW stable, pro-market cultures come from somewhere, not just time. It is not like human nature is hardwired to be cooperative with a million strangers - our instincts are more tribal. I think England or Denmark had it because of things like protestantism, or being generally on the winner side of history, but that is too long to explain maybe in another comment.