Let's assume what Israel thinks is the best case scenario. The ground offensive, which started a few hours ago, is a relatively temporary one. Hamas is dealt a crippling below. The rocket fire stops. The Palestinian Authority, i.e. Fatah, returns to Gaza. Mohammed Abbas is installed in Gaza.
The answer is relatively straightforward. For Israel's southern territory to breathe free again, Israel needs an agreement with SOMEBODY. Neither it nor Egypt has any desire to administer Gaza directly. If it allows a Fatah-led Palestinian Authority to govern, that government must have the ability and the resolve to control the Islamist elements. The chances of that are next to nil.
The only real chance for Israel accomplishing its mission is for Hamas to reinvent itself as something kinder and gentler. The chances of that are next to nil.
What this means is that, in the best case scenario, Hamas will be hit hard, regroup and rearm, this time in a more deadly manner. To eliminate that possiblity – and one can – Israel has to ethnically cleanse Gaza by driving away or murdering hundreds of thousands of potential recruits. It won't do that.