Extended Statistics help the planner with evaluating the query complexity in order to choose the correct algorithm for processing the query. Creating new statistics on a couple of dependant columns in a table probably creates some complex structure somewhere in the database because they have to be refreshed by ANALYZ(E)ing the table. There's a table pg_statistics_ext_data which I can't even view because my master (and only) account does not have the rights to SELECT.
What am I asking is, are they any trade offs to these statistics? Do they take up huge amounts of data on the disk? Can I somehow find out how much?
Why are they not used everytime no matter if I create them manually?
The expense of maintaining and using these statistics grows with the number of columns. Imagine having to track the interdependencies of each pair of columns in a wide table!
The price for extended statistics has to be paid whenever PostgreSQL collects statistics and whenever a query is planned. That's why they should only be employed qhen necessary.