A number of Schema changes and query optimizations could be handled by updating the stored procs without having to recompile the application.
But, I'd argue the API schema gives you better control over this by pushing what might otherwise be application-level logic into the database. I've solved a lot of bad ORM behavior this way.
Unfortunately, modern development favors having all logic on the application side. There are a lot of benefits that brings including better testing (stored proc testing frameworks never really caught on) however I find now a lot of people I work with rely too heavily on the ORM and don't know how to work with the databases (writing sub optimal queries, not properly indexing, etc)
In the example above, the select statements were inside stored procedures, and applications were only granted permissions to execute those with appropriate parameters.