That was not Israel’s policy back in 2006. Hamas had zero interest in coexistence or the wellbeing (or lives) of the people living in Gaza. The current situation is a direct outcome of that.
I mean.. yes, if the only choice is between removing the entire population of Gaza and giving it back to Hamas it’s not that surprising that most Israeli’s are picking the first option.
I don't think the evidence favors this conclusion. Their actions immediately following 2006 suggests they definitely had quite a bit of interest - they enforced a ceasefire after 2006 (also punishing other groups that attempted to break it), and according to former President Carter were willing to accept a 2-state solution if the Palestinians democratically approved it. This was all put on hold after Cast Lead, which aligns with the Israeli policy of denying a two-state solution.
The only piece of evidence I can think of that counters this is Hamas' charter, which IIRC calls for the creation of a Palestinian state in all of former Mandatory Palestine which would imply the destruction of Israel. But even then, based on the pragmatism demonstrated above (and the openness to a two-state solution), the Hamas leadership were rational enough to realize this goal could not be achieved.