Randal Holcombe has an essay at Cato Unbound for the Anarchists to take it easy.
I met Dr. Holcombe at the epicenter of anarcho-capitalism at the Ludwig von Mises Institute's Austrian Scholar's Conference last March, and he is at least 1/2 the reason I'm applying to FSU for grad school. (Bruce Benson is the other half.)
His most important point is,
"there are a number of libertarian anarchists who argue for the complete elimination of government. Their arguments are based on two complementary lines of reasoning. One is that anarchy would work better than government (Leeson’s essay is along those lines, although he doesn’t make claims quite that strong), and the other is that the coercion that underlies all government activity is immoral. I have no quarrel with people who make those arguments, but from a policy perspective they are irrelevant."
Now this centers down on what economics is, and reveals the importance of the discussion concerning methodology.
If economics is only relevant when it produces policy recommendation which are politically feasable, then the academy has a responsibility to produce a certain kind of research. Most importantly, it is completely the servant of the state.
If, however, economics is relevant even when it recommends policies which are politically impossible, then it acts more like a true science - such as physics, or biology. It follows the evidence and the logic to every rational conclusion.
The question seems more focussed on whether economists want to be heard, or whether they want their ideas to be purchased.
As an idealist, I can afford to throw public opinion to the wind. If I ever get tenure, I can likewise throw opinion to the wind. In order to get tenure, ah! we must appease. We must produce something useful. We are forced into a Pareto Paradigm (which might be a good name for a blog or radio show..., but not a rock band) where we are restrained from following every though to its rational conclusion, because to do so would be to accept Mankiw's judgment on Hayek: It's just a slippery slope argument, and its not true.
Most economists need to want to be heard. I may or may not be one of them.