Taking on Hamas by plowing through the area in a broad military invasion is just not the best way of doing it in my opinion.
(On a side note: Hamas is reportedly funded the most from sources in Saudi Arabia, the USA's biggest Arabian ally. Surely something could be done about that. Although I presume good old fashioned greed will make sure nothing significant happens there. :D)
And let's theorize Hamas is officially banned. Will it have much positive effect on the situation? Will terrorist attacks disappear? I think the situation would pretty much stay the same but the 'enemy' will just be called 'Al-Qaeda', 'Hamas underground' or something else.
I don't think every angry Palestinian or member of Hamas is just angry because they hate Jews and want them all dead either. People are mostly angry and become extremists because they're in a shitty situation.
To compress it all into a sentence or two: Pinpoint strikes and better living conditions for people in Gaza, hell maybe they could finally get a country of their own. Either making Jerusalem open to both or to neither.