Warning: escapeshellcmd() has been disabled for security reasons in mimemail_isshellsafe()

This error message says the problem arises in the Mime Mail module, not the Mail System module. This should have been moved to the correct issue queue long ago.

The cause of the error message is your PHP configuration - this is outside of what is controlled by Drupal or Mime Mail. Your PHP configuration (in php.ini) has disabled the use of PHP's escapeshellcmd() function on your server. Mime Mail uses this function, so if you don't allow this function then Mime Mail will not run.

Because Drupal 7 is so old I have no plans to change this code in Mime Mail, as there are tens of thousands of sites using this module without an error and changing some fundamental function call like this has potential to disrupt and/or break those sites. There are no other reports of this error on other sites, so I think the solution here would be to edit your php.ini and remove escapeshellcmd from the list of disabled functions on your server.