I don't think the incentives for politicians are really there, at least not on an individual levels. Most politicians at a national level do not rely on their government salaries for sustenance, so the obvious incentive to be re-elected isn't there. As for the incentive to be re-elected due to desire for power, that's a more promising idea, but even then, the rational ignorance point means that the getting re-elected is not the same as "being judged by the people as a good servant of the people."

As for the evidence that governments work, despite a satisfactory economic model for why they should be expected to, I don't personally see the evidence. I see a lot of evidence the support the claim that governments are overwhelmingly likely to exist, but not that they are the "best" way to organize society (for any given definition of "best").

It works for the same reason a well-administered datacenter does: because the professionals tasked with maintaining[1] it are assiduous in so doing.

[1] http://xroads.virginia.edu/~Hyper2/CDFinal/Lippman/cover.htm...

The economic mechanism that causes well administered datacenters to exist is clear: there is demand for hosting and a (mostly) competitive market attempting to supply hosting. Poorly administered datacenters have a lower chance of staying in business. But if there was a legal monopoly on datacenters (e.g. only the government could provide hosting, and citizens voted on the leadership of the datacenters), I am not aware of an economic mechanism that would cause the datacenters to satisfy demand efficiently or at all.