'wp_handle_upload' Should Create the Resized Versions

I find the ‘wp_handle_upload’ frustratingly useless unless it can also create the various sizes for the images (thumbnail, medium and large).

I’ve searched the web and WordPress files for the last few days now and have found nothing but other people experiencing the same problem. The default media upload is a very powerful feature, but we need this to be available for people creating a custom UI experience with the custom post types.

Would appreciate a solution (not plugins) to this if anyone does have one.