Better mimetype detection, also without MimeDetect module

For my module image_fupload, I need the function "field_file_save_file" in "field_file.inc" to mass import image files. But if the module MimeDetect isn't installed, it is always returned "text/plain" as mimetype. That's a bad idea I think, because Drupal itself comes with a function to determine the mimetype.
So, it would be great to replace the following lines of code

<?php
$file->filemime = module_exists('mimedetect') ? mimedetect_mime($file) : 'text/plain';
?>

with these ones:

<?php
$file->filemime = module_exists('mimedetect') ? mimedetect_mime($file) : file_get_mimetype($file->filename);
?>