But there is a massive risk here. Such a victory will not just achieve Cast Lead's original stated aim, namely altering Hamas's calculus - reducing its incentive to fire rockets at civilian targets inside Israel - but could topple the Hamas government altogether.
Israeli officials deny that regime change in Gaza is either likely to happen or the goal of their mission. But that may end up being the result: intelligence reports suggest the organisation has been eviscerated, its ability to govern all but destroyed.
Israeli leaders will crow at that; their poll numbers will surge. But it will surely prove a pyrrhic victory. For what would be the consequences of crippling the Hamas administration in Gaza? Israel would be confronted with a sharp dilemma. Either it would have to stay, resuming the occupation it sought to end in 2005 - a notion with zero popular appeal in Israel. Or it would have to withdraw, leaving behind a huge and dangerous question mark.
For Gaza could become a vacuum, rapidly descending into Somalia, a lawless badland of warlords and clans. A new force could seek to replace Hamas. Most likely it would be even more radical: al-Qaida has long been pushing at the edges of Gaza, eager to find a way in.
Would either of those options appeal to Israel? Of course they wouldn't. As one Israeli commentator put it yesterday: "In this context the IDF is afraid of being too successful."
Israel's preferred scenario, having pushed Hamas out of the way, is for the pro-western moderates of Fatah to take over. But Fatah knows that to return to Gaza on the back of an Israeli tank is the kiss of death: they would for ever be branded collaborators with the enemy.
Israel may try to dump responsibility for Gaza on a coalition of moderate Arab states and others, including the Fatah-led Palestinian Authority. But would any of them be willing to take it on? Analyst Ahmad Khalidi notes that the "amount of aid, reconstruction and psychological nursing is of such intensity" that surely no one would step in. Israel may be left recalling what Colin Powell once called the Pottery Barn rule: "You break it, you own it".
And from the rubble of Gaza, the attacks on Israel will surely resume. Hamas is too deeply rooted to disappear. New cells will arise, more filled with hatred and bent on revenge than ever. Already there are warnings of a return to suicide bombing, inside Israel and beyond. And, warns Khalidi, there would be no Hamas leadership - with undeniable discipline over its forces and the pragmatism to see the benefits of a ceasefire - to rein in these new, angry fighters. The great irony is that Israel may well decapitate Hamas - only to regret the passing of a Palestinian administration with sufficient stature to bring order.
Perhaps Israel's leadership will see this danger and hold back, pushing for a ceasefire that would be robust and externally supervised but would ultimately, if indirectly, amount to a deal with Hamas. If that is the outcome, it will be a strange kind of victory. For Israel could have got that through diplomacy, without causing the death, mayhem and damage to its international reputation now unfolding before our eyes. If it goes further, it will have removed one danger - only to have replaced it with one far greater.