There's no reason you couldn't add SSL support to a Wordpress droplet created with the one-click image. All the Apache configuration is under: /etc/apache2/apache2.conf You'd just need to add a new VirtualHost that listens on 443 and points to your cert.
The reason that this isn't done by default is that there is no way to do it automatically except for using a self-signed cert. This is not what most people will want as it will cause warnings when you visit the site. Most people will want to obtain a cert from a proper Certificate Authority.
If you want to create your own cert, this article should point you in the right direction:
The Apache web server is the most popular way to serve content on the web. If you need to communicate with your site visitors over a secured connection, setting up a TLS or SSL certificate will enable you to encrypt traffic. In this guide, we'll discuss how to create a self-signed SSL certificate on Ubuntu 14.04 and use it with Apache to encrypt traffic.