Why is this data structure not a more generic tree? It seems as though forcing the data on a tree node to be a specialization of basic_string is needlessly limiting.
Data doesn't have to be a basic_string. You can change it to anything else by supplying different traits to basic_ptree class template. There is an example showing how to use tree with boost::any instead of the string. On the other hand, please note that this library is not a generic tree container - it is intended to be used as a DOM that supports reading/writing multiple data formats out of the box, and gives easy and idiomatic access to the data, without writing miles of supporting code.
What is the rationale for using the word "property" here?
The class is a map from keys to properties (data). I think that idea for the name originally came from java.util.Properties class in Java, which has similar purpose but is flat, not tree-like. Best regards, Marcin