How do I use jQuery to add the TinyMCE WYSIWYG editor to a textarea?

I would just use the WordPress JavaScript API for TinyMCE — wp.editor.

The steps in brief:

  1. PHP: Enqueue the editor scripts (and styles) via wp_enqueue_editor().

  2. JS: Call wp.editor.initialize() from your script.

And do take note of this: (the “this function” refers to wp.editor.initialize)

If this function does nothing, please make sure that
wp.editor.getDefaultSettings is a function.

Which means, if it’s not a function, then while there are no errors thrown in the browser/console, the textarea will not be converted to a TinyMCE editor.