Most of these companies won't have their own proprietary CMS. By the description ("cheap websites") they won't invest in that, and are probably using something open source (read: FREE) or third party solution like <gak> Weebly.
They might not even be doing the work. There's a good deal of businesses (for lack of better word; entrepreneurs? Exploitists?) that simply manage outsourced contractors to do this work in a quantified process. Let the customer choose a free template, give it to a coder, have them build a Wordpress theme around it, have a less skilled person input the content and upload images, done. The only real work is in managing it and sending out the invoices.
It does devalue the work, but there's another side you need to consider: adapt or die. Figure out a division of your work flow to accept similar pricing and procedures. OR, seek a different market that doesn't want cookie cutter approaches and emphasize why this is a better for the client in the long run. What happens then is the lower end cookie cutter producers cease to be your competition.