>Israel doesn't want to control Gaza. Israel want to coexist peacefully with it and has been willing to go very far and take risks to achieve that.
I think it's good to apply Mearsheimer's realist thinking here, and the intention is obviously clear that Israel does not want peace with Gaza as that would require recognition of a Palestinian state as the PLO had wanted since the 70s, which is a non-starter. Instead, as Israel has recognized, it is in its best interest to ethnically cleanse Gaza, either through outright murder of tens of thousands of civilians or rendering the strip uninhabitable to force the Gazans out. Many Gazans live in tents since their homes were destroyed by the Israeli military, and I doubt Israel will allow for any meaningful reconstruction once the war on Gaza is over, and will probably welcome the remaining Gazans fleeing the inhospitable conditions.
This will probably also open up space for new settlements in Gaza that many politicians have already started proposing.
You have to realize that most Israelis (~75%, and this figure includes Arabs) are in favour of the war, and IIRC half are in favour of expelling the Arabs altogether. I don't think we'd see much objection to this course of events within Israel itself.
>The fact that Jordan and Egypt has not seen a single attack after they stopped attacking Israel is well known.
It is interesting you mention this, because during the Israeli occupation of the Sinai penninsula in 1967, Egypt attempted to resolve the issue diplomatically, mediated by Gunnar Jarring. Their request was simply the Sinai in return for recognition of Israel and cessation of hostilities. Israel refused these conditions. Egypt eventually attacked in October 1973 and (much to Israel's surprise) was able to retake enough of the Sinai to call Israel's military domination into question. I think Rabin said that Egypt was enough of a threat that it needed to be neutralized, which is what the Camp David Accords did. It was literally through attacking Israel that Egypt was able to achieve the diplomatic solution it wanted from the start.
>Israel wanted Gaza to succeed and forcefully removed their own people
The Palestinians materially gained nothing from disengagement (in fact, they were blockaded and bombed during Cast Lead and Pillar of Defense despite the "disengagement"), but the Israelis were able to alleviate enough American pressure for a peace process that could potentially result in Palestinian statehood. Not to mention a costly military occupation could be stopped and Jewish settlements in one of the most densely populated regions of the world (i.e. a disaster waiting to happen) could be dismantled.
I don't think benevolence towards Gazans had any role in the decision for disengagement, considering the overall Israeli indifference towards the suffering of the Gazans.