Everyone agrees doesn't imply that something is true. Just take a look at any decent science to see how hard it is to detect causality.

It's quite easy to tell a story of how Giuliani implemented the broken windows doctrine and then crime rates fall. Then it might be that it's all just effects of lead on children brain development. It might be some other random reason. Freakonomics did suggest that it was abortions.

Your history analysis that focuses on governments as actors completely ignores effects such as the environmental effects of lead. There quite a lot that happened in the 19th century as far as the industrial revolution goes.

You are ignoring the meta-level. In the 19th century we got schools with compulsory education and children where taught that nation states are really important. History was told as a bunch of actions of state actors. Things happened because of ministers, princes and kings. If your goal is getting people to believe in nation states that's useful. But that goal is different from the goal of truth.

Niall Ferguson for example manages to tell a quite different history. There's money. The importing of good math notation, allows calculation of new forms of debt. The French Revolution happened because the French state sunk in debt. Bankers amassed a lot of money and picked winners and losers in wars. Many times corruption wasn't even illegal in the early 19th century. Some politicians didn't get a salary because they made more than enough money via bribes.

it risks being one of those serious-sounding cautions that doesn't actually throw much light on situations.

Sometimes the keys just don't lie under the street light.