If all they do is write interesting content and promote it, why do we call it SEO? Last time I checked, that matches the job description of public relations writer.
Those pages can be scattered across the site architect and have improper linking. They can have improper titles, meta descriptions, and image alt tags. Often times writers can't grasp these things, or they are so overworked with pumping out content that they simply don't have the time for them.
SEOs can be more technical, and can also make changes across a large site or networks of sites. EG: Missing the city and state from the h1 of every vehicle landing page for hundreds or thousands of vehicles on a thousand dealership sites can have a dramatic impact.
In this sense many SEOs also have the skills to be what we now call Content Strategists. People that do research, plan, and keep the content teams moving in the right direction.
You touched on the other issue: Even if all you do is write and design, by calling yourself SEO, you're attracting clients narrowly focused on their search ranking. That's the metric they're going to judge your performance on, and it won't matter how accessible you make their site if they don't get the #1 spot for "cosmetic dentistry allentown pa." So by selling SEO, you miss an opportunity to educate clients on creating a memorable user experience.