I'm a web designer/developer with a good grounding in
SEO/SEM (mostly thanks to this forum!) though I am by no means an
SEO expert. I think what you're getting at depends on the company, the client, or a bit of both. I've positioned myself to work with small businesses and nonprofits, and most of my clients need both design work and
SEO/SEM but may not be able to afford both as separate and distinct services. So I offer a smorgasbord of services, and try to give them the opportunity to make good choices by explaining the potential future ramifications. And I guess I'm one of those rare animals who considers that skills across the board in all three areas that Peter mentioned are necessary for me to do my job properly. Yes, there's one I'm best at, but without a fairly thorough understanding of the other two, I wouldn't have the strong following I do.
A lot of times choices made early on can make it easier to create a site that will rank well for niche phrases, and I consider my job to include letting clients know what the upside and downside of each choice is so they can make informed decisions. If they pay attention and use the tools I build for them wisely, they end up with decent rankings and respectable traffic.
I can't tell you how many times a client has come to me wanting an entire flash site on a monster template budget, AND they want to rank well in the SEs. Explaining the realities of all that in
SEO terms, as well as the budgetary issues, is usually all it takes to get them grounded in reality.
That's been my experience. Hope that helps.