Recently I came across a blog post that discussed the aspects of how web design & SEO together can determine the click-through ratio of your site within the search engine results page. Many SEO services companies claim that by simply getting a website up on the first page, a site’s click through ratio is bound to go up. That is true to an extent, but the recent addition of a magnifying glass icon that lets you preview sites on Google before you even 
click on them can once again take you back to the very basics of web design.
A good SEO company will always be a good website design company as well, or at the very least a good consultant in regards to how to do design a website that is search engine friendly. Not only that, but they will know that in order to convert visitors to leads or sales, a website needs to be designed to be not just visually attractive, but also able to provide a great user experience with a high degree of functionality. Most SEO service businesses are selling primarily on the basis that once a site is ranked, your sales are bound to go up naturally. This is true to a certain extent – given that proper initial SEO setup and research was done. However if there is a weak design in place, no matter how many visitors arrive to a page, they are bound to bounce off of it in a matter of seconds.
You can read the blog post that speaks about CTR rates & SEO for a further understanding of how they approached the topics and the various other points they mention in their post to support their claims.