We should always be suspicious of the "public intellectual," the thinker or philosopher or critical thinker who enters too easily into the public sphere. For my own part—unless someone is willing to pay me to be one—I believe there is a necessary tension between being an intellectual and being a public figure.
Of course, Socrates was a sort of public figure, but not a figure of influence in the government or in the shadows of government. He was as much a figure of ridicule and revulsion to the general public as a figure respected. Diogenes played much the same role. When Plato attempted to put himself in league with power, implementing his picture of the ideal state in Syracuse, it was a massive failure.
Montaigne undertook the great intellectual labors of the Essays not when he was still engaged in public life, but having closed himself up in his tower. Nietzsche is right to characterize the intellectual as a lover of the desert, as a kind of ascetic who has the humility of a mother nurturing her child, the child—or idea—for whom she lives.
When the intellectual enters the public sphere too often you end up with Heidegger giving philosophical justifications for the great spiritual awakening he saw in Nazism, or the famous trahison de les clercs in which intellectual elites found themselves justifying the horrors of Stalinism. You get the theater of Christopher Hitchens—who thought himself a disciple of Orwell?—forgetting his own excoriation of Pinochet and welcoming the invasion of Iraq and helping to usher in a strengthened national security state. Speaking of Pinochet, you had the spectacle of Chicago-trained economists fomenting a revolution and welcoming a dictatorial state, all in the name of freedom. Of course, you also had Friedrich Hayek pronouncing that very state one of the freest he'd seen—no word of the thousands who were freed by being murdered. You have American intellectuals, both left and right, arguing that really torture of terrorists is justified by the common good or that drone warfare isn't problematic because, well, even if they aren't terrorists yet, those innocents who may be killed would be in the future. You get professors who praise el Che with no mention of his methods or the necessity of a continuing revolution. And, you get professors who argue that, when gays and lesbians are murdered in the Arab world, it's the Arab world that is the real victim—of Western imperialism and something called the Gay International—and not the people being killed; anyway, their blood is somehow on the hands of gays in the West.
And, you get the phenomenon of Dawkins, et al., mischaracterizing theism and ignoring two thousand years of argument so they might fill auditoria.
Of course, public intellectuals do sometimes do great good. Orwell surely did, Russell may have. But the temptation to publicity is a temptation to power, to reputation, to opinion, even the temptation to be a figure, maybe a controversial one. And, a pursuit of the truth and a pursuit of the expression of that truth—whether it be in the interests of power or not—is almost always going to make one unpopular.
You can be a public figure or you can be an intellectual, but it is damned hard to be both.