Allowing post attachments without allowing to insert in text

One way to do this would be to simply hide the upload/insert media button: and, then add featured image support for your themes posts, so a user can still attach images to the post.

Hide upload/insert media button for your theme in: functions.php:

function hideUploadInsert($hook)
{
    if($hook != 'post.php' AND $hook != 'post-new.php')
        return; // if not in the edit or new admin pages, for Posts or Pages, then do nothing.
    echo '<style type="text/css" media="screen">
        #wp-content-media-buttons {
            display: none;
        }
</style>';
}
add_action('admin_enqueue_scripts', 'hideUploadInsert');

Add featured image support to your themes posts in: functions.php

add_theme_support('post-thumbnails', array( 'post' ));

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EDIT:

I didn’t realize you were referring to attaching multiple images to a post. You could just use the css I gave above to hide the button for inserting images into a post: and, then use one of the plugins that come up in a google search for attaching multiple featured images to a post:
https://www.google.ca/search?q=wordpress+multiple+featured+images