Interesting question, although I am not sure what your end game is. A controller basically 'bootstraps' the framework into a useable state. My experience lies with Symfony, Zend, and CakePHP, and can tell you that the controllers used in Symfony are quite short (~50 lines of code). However the underlying code is quite extensive, but this code does a number of things such as setup your ORM, cache heavily used arrays (creating static files in /cache directory), and initialize an autoloader for file calls, just to name a few.
Within the Symfony Framework context you have a primary controller, but you also have mini-controllers, or as you put it, page controllers, these controllers are referred to as 'actions'. An action acts as a bridge between a user request and various attributes of your application which may include file/data stores, request handling, user redirects etc. As with the primary controller the actions are meant to be lightweight, mainly consisting of API calls to underlying classes and functions.
I have actually used Zend within Symfony to fill the gaps in functionality that Symfony does not provide. So to your question, I am using Zend functionality without any controller interaction. All I need to do is initialize Zend within the autoloader (b/c Zend is correctly namespaced). Also did this with CakePHP to take advantage of the Inflector class, no controller usage, just calls to functionality I didn't want to write myself.
