> But the demand for lawyers is completely cultural.
I don't think that's the case. People think that the U.S. has a lot of lawyers because we're a "litigious society" but I've never seen evidence suggesting that Americans are more likely to sue than other sorts of people.
I think the demand for lawyers is more structural than anything else, and there are a lot of dimensions to this. First, the amount of conflict rises proportionally with the number of interactions between people. This means larger societies have more (superlinearly more) conflict than smaller ones, more active economies have more conflict than less active ones, and heterogenous societies have more conflict than homogenous ones.
Second, different countries use different mechanisms to accomplish the same tasks. The U.S. is at one extreme--we use private litigation to handle things like employer/employee disputes that might in other countries be handled by a complaint to some sort of board. Litigation is, by design, the way to challenge most government action. In the regulatory regime, we skimp on government enforcement of things like financial or enviromental laws, and write in "citizen suit provisions" to allow private enforcement.
Third, the demand for lawyers depends on the structure of the economy. An economy based on financial services, which can result in expensive and complex disputes, needs many more lawyers than one based on agriculture.
Fourth, the number of lawyers in a country isn't directly proportional to the amount of conflict within the country itself. A country that hosts numerous multi-national corporations will have many lawyers working on disputes that actually arise in other countries. Moreover, a country with a sophisticated legal system will be asked to resolve disputes that only have a tenuous connection to the country. The U.S. is also a net exporter of legal services, in conjunction with its export of financial services. American firms do work for Brazilian companies doing IPOs in Brazilian markets. The reverse is never true.
An example of an (industrialized) country that has 1/10 as many lawyers per capita as the US is Finland. Can you compare the US with Finland? The US has 133 Fortune Global 500 companies, Finland has 1. The US has 9 cities as large or larger than Finland. The U.S. is extremely heterogenous. Finland is extremely homogenous. The US has to alter its laws to limit the number of foreign cases coming into New York City's courts (a city 4x as large as Finland). An American (or sometimes UK) firm is involved in some way in nearly every major IPO that happens in one of the world's large financial markets. How many Finnish firms are involved in American IPO's? Etc.