I've heard two main benefits of academics writing for a popular audience: improving the clarity of your writing, and building your overall reputation.
In terms of clarity, two friends and I spent a few months writing for an imagined general-interest audience, and our experience shared a common thread that, though still amounting to little than anecdotal evidence, was illuminating for me: our writing did become more clear over time. I think it is the difference between reading and teaching, in that as we worked to master an idea enough to "translate" it for a non-technical audience we had to understand our own ideas on a more fundamental level, compared to writing academic material where we assumed the audience was more knowledgeable in the specific subfield than ourselves and hence leaned more on the reader and less on our own presentation.
On the second benefit, I think it is important to remember that academic careers are built on both publications and reputation. The former is more cut-and-dry in terms of tenure and hiring, but the latter still plays an important part in creating opportunities to stick out compared to similar academics in specific instances (e.g. being remembered by a senior professor from a shared conference presentation, discovering at a dinner that you and the journal editor grew up in the same town, the chair of the hiring committee remembering a humorous blog post you wrote about a recent university hiring freeze, etc.).
Writing for a more general audience is also where many academics hope to make "real" money later in their career, and so practicing the art of writing for a non-academic audience seems to make sense given such a later goal. In this day of bring-me-an-existing-audience-and-I'll-invest-in-your-personality-as-product, where a popular blog can be a realistic springboard to more general audience opportunities, I think that writing for a popular audience makes sense as the first step towards creating a brand around yourself (á la Steven Levitt or Jared Diamond or Nate Silver), but it is only the first step: the second step, actually creating a following around your writing, is even more important than just producing the material for this strategy.
As a side note, I found a wonderful rant about the tension within academia regarding of popular writing, posted by Yale grad student Madison Moore: "It all boils down to this: certain kinds of elitism are tired and old by now. We are in an age when nobody reads the whole paper—they skim the headlines in Google Reader all at once . . . With every unreadable text, every whopping three copies sold of an 'earth shattering' book on the representation of menstruation in medieval literature, academia will continue to fight for relevance. A professor once told me that as long as three Victorian scholars in the field read his book and it changed their research, he would be happy. He 'doesn’t care about the housewives of Tennessee.' That’s what he actually said."
You might also enjoy historian David Greenberg's discussion on the mixed envy-meets-criticism from academics for commercially successful scholarly authors.