The only way this could work would be ?post_type=any based on WP_Query post_type params.
But the context is the problem, the edit.php page requires a specific post type, to display and edit only one $post_type_object which returns, for each post_type, only one singular label, one plural label and so many others individual properties.
These are not only technical blocking problems but also conceptual ones which make this impossible to be done.
Personally, I would research on “How to build a custom admin page” with a query like post_type=any