Regarding the thread question:
It is unknowable if Israel can destroy Hamas (and the Gaza contingent of Palestinian Islamic Jihad), so one cannot make a case. But even if Gaza is cleared of every trace of the current militant outfits, a new one will appear.
I think it is more practical, and really essential, for Israel to stop the tactics that have worked for the militants/terrorists.
So I think the Israel Defense Force (IDF) has little choice but to stop the rockets that continue tonight to be fired from Gaza at Israel. I expect they will succeed there because there is no real alternative.
For many years, there has been, month after month, rockets, and firebombs, and other projectiles, launched from Gaza to Israeli towns near Gaza, especially Sdorot (population 31,000). Fewer than this week? Yes, but enough so that it is hard for me to imagine living under that threat. Israelis – mostly lower income Israelis – who lived there effectively made an unsigned deal with the rest of the nation where they, with their presence, showed that Jews were not driven out of a corner of Israel. In return for the security risk they took, they received low housing costs. Part of the implied deal was that the Israel Defense Force would prevent any mass casualty event. Unless Israel is willing to effectively cede the region near Gaza – and they are not – it is now necessary to establish that the area is much safer than before. Otherwise, residents will never return. Doing this requires a real halt to incoming mortars and rockets.
Will it require a long-term occupation of Gaza? I hope not. One possibility is a technical fix, later this decade, in the form of laser missile defense. If this works as hoped, the cost of shooting down a rocket or mortar will be so much less than the cost of the projectile as to make current tactics, I hope, impossible. A very different possibility would be a Gaza peacekeeping force.
P.S. Of course Israel has to prevent another cross-border attack, but perhaps they have already started that by mining the border with Gaza and/or will find other technical means.