Implicit in Mr. Benn’s argument, however, is that the only way to stop Hamas from gaining legitimacy is for Israel to fully occupy Gaza again, more than three years after removing its soldiers and settlers. That is a prospect practically no one in Israel or abroad is advocating.

Image Israeli soldiers took position on Saturday before entering Gaza at its northern border. It is not clear whether Israel hopes to overthrow Hamas, or who would lead Gaza if Hamas were ousted. Credit... Ravid Biram/Agence France-Presse — Getty Images

Moreover, while it may sound decisive to speak of taking Hamas out of power, almost no one familiar with Gaza and Palestinian politics considers it realistic. Hamas legislators won a democratic majority in elections four years ago, and the group has 15,000 to 20,000 men under arms. It has consolidated its rule in the past 18 months since pushing out its rivals loyal to the more Western-oriented and moderate Fatah party of President Mahmoud Abbas, who sits in Ramallah in the West Bank.

And while there are plenty of Gazans who would prefer Fatah, they seem hardly organized or strong enough to become the new rulers, even with the help of former colleagues in exile in Ramallah who say, anyway, that they would never be willing to ride into Gaza on the back of an Israeli tank. In fact, the longer Israel pounds Gaza, the weaker Fatah is likely to become because it will be seen as collaborating.

The likelier result of a destruction of the Hamas infrastructure, then, would be chaos, anathema not only to the people of Gaza but also to those hoping for peace in southern Israel.

Yet in its campaign so far, which has killed scores of children and other bystanders, Israel has not spared the trappings of Hamas sovereignty or limited itself to military targets. It says that the mosques it has destroyed were weapons storehouses and that the Islamic University, which it has hit repeatedly, housed explosives factories. But it has also reduced many government buildings to rubble without any claim that they were military in nature.

“The government buildings are a place where financial, logistical and human resources serve to support terror,” said Capt. Benjamin Rutland, a spokesman for the Israeli military. “Much of the government is involved in the active support and planning of terror.”

Taken together, it suggests that even if Israel intends to hold back from completely overthrowing Hamas, its choice of assault tactics could head that way anyway. And the Israelis may already be facing a kind of mission creep: after all, if enough of Hamas’s infrastructure is destroyed, the prospect of governing Gaza, a densely populated, refugee-filled area whose weak economy has been devastated by the Israeli-led boycott, will be exceedingly difficult.