Granted, in practice their implementation probably does not live up to the words I used. But...
Mail delivered media cannot compare to the speed, reliability, flexibility, or scalability of a live, accessible, database. Not to mention the history of FOIA requests handled by people that are often resisted and combated leading to inaccessibility and/or court battles.
You cite a single request from a single person, but you cannot physically provide the sort of instantaneous daily reporting that hundreds, thousands? of groups and/or individuals would ask for. Imagine the internet if google had to mail you media of every single search result. It's not the same service, it would not meet public data standards for this day and age.
Across the federal government, the same open source standard for front end delivery could be deployed. Management would be minimal with shared costs for savings, and practically no man hours for individual requests. The biggest challenge would be data entry from the sources, but that is a cost that already exists. Ultimately, I do think a web accessible database is highly efficient and cost effective.