If an organization provides Blackboard for their faculty, then they're much less likely to also provide other services that accomplish the same general goal (like private web page hosting, course-specific fileshares, etc). IT departments don't like having to maintain redundant services. In those environments, users generally don't have any other option than Blackboard.
I believe the real question is why Blackboard in particular is so popular. A big reason for this is that Blackboard was one of the first CMS systems available that focused on the educational sector. Educators could try it out for free and since most schools didn't have any sort of CMS at the time, IT departments got a lot of requests for it. Over time, Blackboard has bought out several of their largest competitors, further entrenching themselves and making it more difficult for a rival product to compete. Blackboard also had a patent on an "Internet-based education support system and methods" that they've used to scare off competitors (the patent was eventually ruled invalid).
The real competition in this space is from open-source systems like Moodle. They're insulated from the problems listed above since they don't live or die based on market share, and since Blackboard has pledged not to assert their patents against open-source or non-profit entities. Unfortunately, it's hard for an open-source CMS to gain the same traction as a proprietary product like Blackboard, regardless of the quality of the product. Blackboard puts a lot of resources into advertising and marketing, and open-source projects generally can't come close to matching that. Decisions about which CMS to use are generally made by high-level management (not IT, faculty, or anyone else who actually has to use it). These folks aren't likely to even know what "open-source software" is, much less what options are available, so they tend to base their decisions on what they hear from sales representatives. If there was a company behind Moodle that was pushing it as aggressively and consistently as Blackboard, I have a strong feeling that you wouldn't see Blackboard anywhere near as often as you do now (surveys frequently show the overwhelming majority of blackboard users don't like it).
This isn't a unique tale. You can replace "Blackboard" above with the name of almost any other piece of "popular" enterprise software and the story is pretty much the same.