I didn't rule out showing off, I ruled out worldwide fame. People find communities that they believe to be important and then seek to gain status in those communities. You don't care about who won the best rhubarb pie in the greater Kansas bake off, but there is small contingent of people who care greatly about this prize. (After all, Kansas is center stage for fruit-based pies worldwide, and everyone knows that rhubarb is the true test of the purist.) This effect is even stronger in academic fields where it's easier to convince oneself of the importance of your community even when most people haven't heard of you. (The masses just don't understand the importance of our work, obviously.)
It's not always easy to distinguish between status motivations and the more socially desirable motivations. In fact, one measure of how well our institutions are constructed is how well aligned these motivations are; ideally, they would be indistinguishable. But there are ways to tease this out.
For example, when some exogenous input (e.g. federal funding cut) knock these people out of a high-status career, do they still work long hours in their spare time on the subject? Very rarely, especially as it becomes clear they won't regain former respect.
The incredible power of fads in academics, even among those with tenure, is more evidence. The best group strategies for maximizing impact call for diversifying research routes, but academic researchers clump very strongly because this is often in the best interest of an individual's status.
Human motivations are complicated and this makes it very difficult to compile indisputable evidence of anything. This is compounded by the fact that we want to appear to have other motivations than our actual ones. However, I think if you take a careful look and try to model academics as robots you'll find the "tries to maximize status" is a better first order approximation than "tries to maximize academic contribution".
For the record, I've been strongly influenced by the views of economist Robin Hanson on this subject.