It's not possible to set page title via hook_page_build or hook_page_alter

I'm not sure if this is a bug or it is intended but it is not possible to set the page's title via hook_page_build() nor hook_page_alter() because the title it saved into a variable in the beginning of the drupal_prepare_page() function and it is set at the end of the function so implementing any of the aforementioned hooks to alter the page title won't change anything.