With the rather strict definition of SEO you seem to hold, and a very high-level definition of concepts, your above comments make sense. Yet, in practice, SEOers get involved in a larger number of areas than just figuring out how to optimise organic search, they get involved in the general role of getting more targetted visitors to the site, so pure technical search engine blackbox testing is one skill in their toolbox.

They get involved in the AdSense part of search engines, where changes in advertising wording affect the number of people clicking on that ad. A marketing department most likely wouldn't be able to come anywhere near an SEO who knows what audiences are searching for and the material on their site that matches that criteria. The flexibility and quick reaction times here, a decent SEO will outscore a "big campaign" focused marketing department.

So funnel optimisation then can be on the remit of an SEO - the funnel between the website, and the conversion goal (getting the right people from a search engine results page to the right piece of content. The route is an essential part of it - do people get there directly, or via an intermediate page - will marketers have sufficient technical knowledge and understanding of searching patterns to make a good decision?)

So in terms of funnel optimisation, of course, testing and optimising content that people see to increase conversion rates - it makes a great deal of sense to have an SEO involved.

Analytics - yes, it's the tool that measures the effect of SEO. But who is going to set that up accurately? Whose going to know what beacons/shims are needed where to be able to measure the effectiveness of their work? If anyone, SEO are quite the right group of people to ensure that beacons are in the right places, and remain in the right place, adjusting, correcting and improving as the site and it's traffic grows. I don't see a marketer, a web developer or an engineer having the inclination or dedication to keeping that running optimally.

Content strategy - do you really want product reference and howto guides in the hands of marketers? Seriously? Sure, for a brochureware site right before the signup, I guess marketers should be substantially involved here. But the support material? SEOers are well placed to connect the right support material with the people looking for it.

Reputation tracking - I'm not convinced this is entirely in the remit of PR - they are likely to ignore a handful of complaints in tweets in favour of the bigger picture. Best get a customer servicing person involved. And a couple of well thought out tweets and conversations from a knowledgeable SEO wouldn't go amiss either.

Competitive research - again, at such a high level fine, pay some consultant. At the "why is their website doing better than mine" an SEO will outdo a marketing consultant any day.

Social media marketing - again, you're focusing at a far to high level. PR/Marketing aren't the right people to tackle customer servicing issues that surface in social media conversations. And talking to the listening audience on Facebook and Twitter - the key is to do it with a human voice, not a PR/Marketing filtered voice.

Syndication - Legal? On a high-level approach on contracts/agreements between organisations for syndicating content (like AP news items), yes you should involve someone from legal. But tweaking your RSS feed?

duplicate content issues - I'd be very impressed if there was anyone working in a legal department on legal matters who could explain where there were duplicate content issues on their employer's site and recommend a good way of correcting / addressing that. My long experience of lawyers is that they believe deep linking is a breach of copyright.

You're focusing on a too high-level definition of these various aspects of running a website. An SEO is a very handy person to have around in the trenches. Whereas at the high level you are considering this, what PR, Marketing and Legal provide is close to useless on a day-to-day basis.

An SEO person is invaluable at the very granular level, the day-to-day issues that make a website work. PR, Marketing and Legal aren't good at working at such a fine-grained level.