I have a different take, after reading the recent post of my friend and colleague Josh Blackman, about the Arc of the Public Intellectual. It seems to me that the real dynamic is about tradeoffs. Upon getting tenure, professors who write in law and related subjects are fortunate to encounter a “choose your own adventure novel” situation. You can continue to focus on scholarship above all else. Or you can focus on any number of other things, ranging from gaining experience in academic administration (for those who want to be Deans someday) to building a social media brand. It all depends on the goals you set for your career.
Tradeoffs are inevitable, however, as all of these options tend to be time-consuming. The more you focus on one thing, the less you focus on another. So I don’t see the publiic intellectual role as an “arc,” or some kind of inherent pattern, as much as a continuing choice for how professors want their career to run. In my own case, for what it’s worth, I have tended to do less media over time. I concluded that, unless a news story happened to be directly about my area or academic expertise, media appearances weren’t likely to make a difference and were largely a waste of my time. But different people will answer that differently, and the answers can vary over time.