Calling theme_hook_suggestions inside template.php I am using template_preprocess_block() to introduce a theme function like this:

$variables['theme_hook_suggestions'][] = 'block_system_main_front';


but adding MY_THEME_block_system_main_front() to my template.php file does not change anything, MY_THEME_block_system_main_front() is not being called.

How can I introduce a custom theme function using theme_hook_suggestions and then use it like I use theme_image_formatter() ?
theme_hook_suggestions is not for function suggestion, it is for template suggestion.

In your case:

$variables['theme_hook_suggestions'][] = 'block_system_main_front';


Drupal will try to load the file:

your_theme/templates/block-system-main-front.tpl.php