How do I implement hook_page_alter() in a module?
Try using hook_page_build(&amp;$page). hook_page_alter(&amp;$page), which is called directly after it, is meant for themers to use after all the modules are finished with their business.  

I just implemented function MODULE_page_alter(&amp;$page), and it worked in the module as expected.
Did you clear the cache so the module is registered?