I'm an unabashedly open proponent of SEO; I think it's simply the most cost-efficient, effective long-term marketing strategy a business can adopt (in most cases), and the data can largely back me up. I can cite case studies of businesses that have risen high in ranks, earned tons of new referral traffic from external links, and of course organic traffic, and tie those metrics to conversion ratios and customer values to calculate a rough ROI.
But SEO has even more benefits than that. For most search optimizers, everything begins and ends with traffic; an increase in traffic is a sure sign that the strategy is working, and without ample traffic, the strategy is useless. I don't believe these things are true, because there are more secondary and peripheral benefits that people neglect. Why do they neglect them? Because they're almost invisible, in the sense that they're notoriously difficult to measure.
In SEO, brand visibility is achieved in a few different ways. First, there's offsite SEO. When you build links and write up guest posts, you're positioning your brand for the masses. In addition to the authority you gain and the referral traffic you receive, anyone who sees the content will become more aware of your brand. Second, there are search impressions; just because someone didn't click through on your result in the SERPs doesn't mean he/she didn't see you.
However, the prevalence and value of brand visibility are terribly hard to measure. There's no objective, quantifiable scale for how "aware" a person is of your brand, nor is there a convenient way beyond surveys and random sampling to gauge how many people within a target audience are aware of you. Still, SEO does improve this quality, and it shouldn't be ignored when you're considering the full effects of an SEO campaign.
For example, your offsite work (including guest posts and social media marketing) can help show people that you know what you're talking about, and that you're a trustworthy source in the industry. Your page titles and meta descriptions can also form users' first impressions, giving users a "sneak peek" before clicking into your site. Collectively, SEO can make it so the average user comes into your site closer to a final purchase than a user who happened to stumble upon you. Brand reputation also lends itself to social confirmation; users who hold your brand in high esteem will be more likely to recommend you to others in their lives.
Again, brand reputation is hard to measure. Short of asking every user how much they value your brand, there's no definitive way to get a read on this. However, SEO offers brand reputation increases in a compounding pattern; the more work you do, and the more relationships you'll established, the more impressed your inbound users are going to be.
It's definitely true that you can pursue user experience design improvements without SEO, but thanks to Google's natural preference for sites with good user experience, high-functioning site layouts are a natural byproduct of your SEO work. Think of it as killing two birds with one stone; you'll optimize your site for speed, make sure all your content loads effectively and isn't duplicated across the site, and you'll keep your site navigation tight, simple, and intuitive. Simultaneously, you'll be helping your site rank higher in searches and giving your users an all-around better experience to increase conversions.
You can't log into Google Analytics and see definitive, numerical measurements of these benefits, but they are there, and they do add value to your SEO campaign. They shouldn't be your first priority, clearly, as traffic truly is the most important and measurable end result of the SEO process. However, these benefits should all be on your back burner, factoring into your evaluation of ROI as well as your overall strategic approach.