The simple answer is because no single OS meets all needs. Even in the case of Unixes, different flavors have their strengths and weaknesses. Solaris is a solid Unix. If you want to buy your hardware from IBM because you like the new blades, but you have admins that are much more familiar with Solaris than AIX, it might very well make sense for you to get Solaris loaded rather than AIX.
I've never been a really big fan of Solaris on X86 hardware, but will admit that it likely has gotten better than it was when I last spent considerable time trying it out.
You're a bit mistaken if you're thinking the majority of the server market was owned by Linux, BSD, and Microsoft. There is a lot of the above out there, but you'll also find rather large installations of AIX and Solaris backend servers doing serious heavy lifting in datacenters. We use a lot of Oracle running on Solaris in our shop, largely because everyone is comfortable with it. It is a proven combination for us that we're not likely to abandon without some serious thought an experimentation put into it.
In many orgs, you will see a lot of the customer-facing hardware running on BSD and Linux, because most of the apps that are customer facing are web-based, and these types of apps run great on both BSD and Linux. Which of the two you see more in any given shop is largely dependent upon in-house experience and preferences. Where I work, we're migrating from Solaris to Linux on http and some app server stuff (weblogic primarily) because it makes sense from a cost perspective. We also have some large applications that run on AIX that I doubt we'll see move to anything else because you just don't mess with revenue-generating hardware unless you have to.
I think the short answer to your initial query is that inertia is a rather strong (though not insurmountable) force in datacenters. Heavy lifting tends to be done by bigger iron, and that means IBM, Sun or similar companies. Smaller, less critical tasks will generally be assigned to servers running less robust OSes like Linux and Windows. I've seen uptime on AIX and Solaris boxes measured in years. I don't have a lot of personal experience with BSD but I wouldn't cast any aspersions against it and would rate it as more secure and stable than Linux based on the recommendations of people I know and respect.