FriedGreenTomatoes2
This becomes a circular argument. The hostages have only been taken because HAMAS have been allowed to exist.
HAMAS must be completely eradicated. Either by Gazans themselves, or the IDF. But eliminated they must be.
Hamas might be eliminated in their current form, but their ideology will never be eradicated - not while anybody still alive remembers what's happened. If anything, Palestinians and their descendants for many generations will hate Israel even more.
Unless Israel wants to kill all Palestinians, it will always have territories on its borders with people who hate them. It needs to defend its borders (better than it obviously has done) and accept the situation for what it is. Trying to control territories full of hostile people would be eye-wateringly expensive in terms of money and lost Israeli soldier lives. Even with US support, I doubt if Israelis want that. The cheaper option is to bolster the defences.