Disable drag and upload in Media Library

Instead of removing upload script you can make the upload error out if the user does not have admin privileges. Like this-

function tomjn_only_upload_for_admin( $file ) {
    if ( ! current_user_can( 'manage_options' ) ) {
        $file['error'] = 'You can\'t upload images without admin privileges!';
    }
    return $file;
}
add_filter( 'wp_handle_upload_prefilter', 'tomjn_only_upload_for_admin' );

For other possible way please follow this answer- https://wordpress.stackexchange.com/a/105558/59760