IS there any reason not to include javascript in my own post’s embeds?

Does this mean that including JavaScript would be a bad idea?

No, it doesn’t.

That class is used for styling purposes so that you could apply styles specific to when JavaScript is not available (either not supported or is disabled), and when it’s available (supported and enabled). And in most cases/implementations, when JS is enabled, the no-js class will be replaced with js. (I mean, you can use another name, if you want to…)

/* Sample CSS. Allows you to have something like:
  <p class="hide-if-js">Hidden if JS is enabled</p>
  <p class="hide-if-no-js">Hidden if JS is not enabled</p>
 */

.js .hide-if-js,
.no-js .hide-if-no-js {
    display: none;
}

And for the WordPress post embeds, here’s the code which replaces the class name — but only if certain conditions are met (e.g. window.addEventListener is supported by the browser):

document.documentElement.className = document.documentElement.className.replace( /\bno-js\b/, '' ) + ' js';

In fact, WordPress admin pages also use the same trick and you can see the relevant code in wp-admin/admin-header.php:

<body class="wp-admin wp-core-ui no-js <?php echo $admin_body_classes; ?>">
<script type="text/javascript">
    document.body.className = document.body.className.replace('no-js','js');
</script>