Depending on how sympathetic you feel toward the "good men" in question, you could refer to them as Oblomovs, after the titular character in Ivan Goncharov's novel Oblomov (1859). As the Wikipedia article on Obolomov observes,
Ilya Ilyich Oblomov is the central character of the novel, portrayed as the ultimate incarnation of the superfluous man, a symbolic character in 19th-century Russian literature. Oblomov is a young, generous nobleman who seems incapable of making important decisions or undertaking any significant actions.
As this excerpt suggests, another term that might be applied to "good men who do nothing" is superfluous. The term Oblomovs tends to arise in the context of discussions of Russia (naturally), but it does sometimes come up in broader discussions of psychology and philosophy. For example, from an essay on freedom in Erik J. Olsson, Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi (2006):
... our becoming decadents and "wastelanders," nothing to stop ourselves from committing rational suicide, nothing to stop us from becoming Oblomovs but further commitments of ours.
From Mordecai Richler, Joshua Then and Now (1980):
There seemed at first glance, to be a few of the very, very rich in Barcelona, many who were unspeakably poor, but hardly any middle class to speak of. The rich he discovered, were for the most part vastly entertaining fellows who had never done a day's work in their lives and were offended by the very notion of it. Oblomovs abounded. Among them, the engaging but People gathered mindless Antonio, who wore a Savile Row suit and drove a sparkling white Austin-Healey. "Given the benefit of a couple of drinks," Antonio said, "we're all republicans here. A few more stiff ones, and we're Communists. But come four o'clock in the morning, man, every self-respecting Spaniard is an anarchist. So we need Franco, don't you see?"
And from Wales, issues 1–47 (1958[?]) [combined snippets]:
Their output is just enough to personally satisfy on the score of competence (a gesture rather like flexing one's biceps), while adding nothing to the growth of national culture. This purely nominal genuflexion to literature is a symptom of the disease that afflicts all Welshmen culturally. Their day-dreams of achievements are so much more satisfying than any real achievement could be . . . they do not bother with the realities.
This is the fatal flaw of the Welshman. It would not be untrue to describe the Welsh as a race of Oblomovs.