Web design encompasses many different skills and disciplines in the production and maintenance of websites. The different areas of web design include web graphic design; interface design; authoring, including standardised code and proprietary software; user experience design; and search engine optimization. Often many individuals will work in teams covering different aspects of the design process, although some designers will cover them all.
It is true that mobile friendliness is important for SEO. It’s a ranking signal in both Google and Bing’s algorithms when it detects a user is searching on a mobile device.
While designers may primarily focus on the non-text elements of your site, it’s important that they choose fonts and sizes that are easy for your visitors to read.
Page speed is another important aspect of the mobile era. Users may be impatient, or their mobile data connection may not always be reliable.
The degree to which your designer has control over your site architecture will vary based on how involved your SEO is in the process, but it is critical to your site's capacity to rank.