SEO and web development skills are both needed if you want to do SEO correctly on your own websites, to find SEO and dev mistakes you have to understand how the developer could have coded the page and what mistakes may have been made.
I have done a fair bit of SEO work for large corporate clients in the last 8 years and in my experience about 80% of blue chip companies, do not make sure their CMS website is designed to be search engine friendly when they originally have the website commissioned.