I appreciate the idea because I had it myself -- we thought about this when first naming the classes.  But unfortunately I have to oppose the idea because, upon further discussion back when we were making these pages, we realized that there are two main problems with doing this.

First, it would cause problems with alphabetization.  On category pages, for example, all of the Fallen classes would appear under "F" rather than the appropriate letter (such as "D" for "Dreg").  Not much of a problem now, but it could certainly become a problem for readability and simplicity on category pages down the line as more species and classes are added (including in subsequent Destiny games).  Of course this can be fixed by adding alphabetization overrides in the categorization fields of each article, but again this would present problems in terms of volume and consistency later on.

Second, titling class articles with the species preceding the class title violates our Manual of Style's requirement of precision and brevity of article titles.  The most obvious consequence of doing this would be a potentially improper implication that there is more than one kind of "Dreg," more than one kind of "Vandal," and so on.  Where there is a possible ambiguation (such as with "Captain" or "Knight"), we've added the parenthetical for clarity and will add disambiguation pages if and when they become necessary.  (This is probably why the naming convention seems inconsistent at first blush, but it is actually entirely consistent with the naming conventions of the rest of the wiki and the MOS).  But if we changed the naming convention to include the species as well, we would need to add disambiguation pages and explanations for all class articles, which would be a real drag and could potentially even add further to reader confusion. 

It's important to remember that many of our readers are not at all familiar with Destiny and are trying to become more familiar -- the nature of any particular class is obvious from both the species pages and within the first sentence of each class's article.  I think that the benefits of the current naming convention outweigh the cons and any aesthetic benefits we'd experience from changing it. 

Please keep it up with the ideas, though!  Creative solutions to the issues we face are ALWAYS appreciated! :-)

Thank you! I see how it all functions with the larger schema in retrospect. :P