Why doesn't PHP's max_persistent setting limit the total number of ODBC connections to my database?

Refer to Why does phpinfo() display Active Persistent Links of 0/1 when I know there are more open connections to my database?

The max_persistent limit applies to each HTTP server process. Setting max_persistent to 1 doesn't limit the total number of ODBC connections to 1. Eventually, all the HTTP server children will probably have 1 connection to the database.