How to actually set a maxlength for textarea field in contact form
The Form API does not allow to set a maxlength on textarea field types [while plain HTML does]


That's not strictly true....HTML5 introduced a maxlength property for textareas, previous versions do not have it (see https://developer.mozilla.org/en-US/docs/Web/HTML/Element/textarea). 

The default templates that come with Drupal 7 all use XHTML, so the lack of explicit support for HTML5 makes perfect sense.

As long as your doctype is HTML5, this will probably work:

$form['element'] = array(
  '#type' =&gt; 'textarea',
  '#attributes' =&gt; array('maxlength' =&gt; 200),
);