All along, the Herman Cain campaign — which Politico called “one of the most hapless and bumbling operations in modern presidential politics” — has been riveting but improbable. Yet whatever the ex-restaurant executive’s other misdeeds and missteps, Cain’s bid seems finally to have crumbled because of extensive coverage of a woman’s allegations that she had a 13-year extramarital romance with him.

Some Cain supporters have cried foul: “Private, alleged consensual conduct between adults,” said his lawyer, Lin Wood, is “not a proper subject of inquiry by the media or the public.” That’s a point worth examining. Why isn’t this private? How much should the news media care about a past amorous liaison? As Brad Hirschfield asked in his Washington Post column, “Does it matter if Herman Cain had an affair?”

The general argument for exposing personal misconduct is that it sheds light on the candidate’s fitness for office. There’s trustworthiness: If he’s cheating in private, he’ll cheat in public. There’s hypocrisy: The candidate is happily posing as a moral exemplar on the podium while texting his latest squeeze. The hypocrisy rationale is popular among news editors; a survey in the ’90s found that while one-third would report a candidate’s infidelity on general principle, 94 percent would do so if the candidate had explicitly preached “family values.”

There’s recklessness, a word used in conversation by one of The Miami Herald reporters who revealed the brazen dalliance of Gary Hart, Democratic presidential frontrunner in 1987: What was he thinking? Has he no judgment?

And there’s “character.” Character describes moral worth, a supposedly seamless continuity between private and public selves. The candidate who is the “kind of person” who would deceive a spouse is unfit to serve, not because messing around reflects on dedication and competence, but because high office isn’t only a job, it’s an honor, which we confer on people not just because they’re capable, but because they’re deserving.

For its part, the public is conflicted. They don’t like dirty little secrets, but they don’t like the media to spend a lot of time ferreting them out. A 2009 Journal of Mass Media Ethics survey found 62 percent believed “it is important that we know about our public leaders’ private lives,” while 65 percent said the media dwelled on them too much.

Surveys in the ’80s and ’90s found majorities thought infidelity unrelated to presidential capacity and disapproved of media coverage of extramarital affairs. But the JMME survey by Bartosz Wojdynski at Virginia Tech and Daniel Riffe at Chapel Hill found public tolerance of such coverage rose dramatically between 2001 and 2009. The percentage of people (a sample drawn from a single Southern state) who wanted no coverage of private lives fell from 59 to 36 percent, while those who believed it was the media’s job rose from 37 to 58 percent.

“The public expects, at least accepts, mainstream print and broadcast media to shed light on behaviors and issues that may be perceived as personal, even if this means coverage of tawdry affairs . . . ,” the authors conclude. So the audience is willing, which suggests market motives as well as moral ones for coverage.

But there is another side.

After all, it’s hard enough for the electoral process to do its minimum civic role, which is to illuminate public policy alternatives and select people who will handle official duties wisely and effectively, without policing private purity, too.

The notion that private misconduct foretells public performance is appealing, but dubious. The roster of great leaders includes many who were abusive, philandering drunks at home and visionary statesmen at work. Exploring that paradox is what biographers do. Ignoring it is what voters do.

There’s a further problem. If the media accept that private sexual misconduct is deeply revealing of fitness for office, they would logically be obligated to do way more than give big-time play to such allegations if they cropped up. Their duty would be to run hard after infidelity.

This would be a front-burner concern. Coverage resources would have to be redeployed. Fairness would compel sexual scrutiny of other candidates. And that would mean a kind of keyhole-peeping, sheet-sniffing journalism well beyond any we’ve seen in this country, and encourage a redirection of the public gaze that would harm both culture and politics.

I hope we’re not going there. But I fear the lesson of the Cain campaign is to elevate infidelity as an electoral issue and move coverage a big step farther from civic purpose and closer to celebrity-mad tabloid TV.