The problem with your little fiction is that Israel withdrew unilaterly and there is no safe side as the bombing in Tel Aviv last week proved.
Also Israel need not keep day to day management of any Arabs but only keep the area secured.
Notwithstanding, by your definition, Israel continues to maintain management of these same arabs because the World insists Israel provide many of them with employment.
Finally even if your first part was legitimate as the carrot, then the second part, the stick, should also be valid.
But your second part is pure fantasy.
In sum Israel surrenders for no gain and plenty of potential loss.
The border has to be sealed.
And, the bombing in Tel Aviv has to be answered by moving the line.
Fail to seal the border, fail to exact a price in territory, and the attacks will only continue.
You can blame international and US pressure for failing to take a certain measure, and you may be justified. But failing to take that measure guarantees that the attacks continue.
Sharon built the fence in spite of pressure. You have to shut off land access to Israeli territory, whatever the pressure. The only access to Israel must be by air, none at all by land.
I have said in the past that there will never be an independent West Bank. I continue to say it. The West Bank is not viable on its own and will never be. But the answer to that is not for Israel to provide employment at the cost of continued suicide attacks.
Seal the border, and the West Bank will be forced to look to Amman for its employment and markets. Not a great option, but also not Israel's problem. Jordan doesn't want the territory, but again, not Israel's problem if they seal the border, and force the arabs to deal with one another.
Seal the border, and Gaza will be forced to look to Egypt for its employment and markets. Egypt says they don't want the territory, but they are already eyeing it. You have to make it not your problem, and you do it by sealing the border to all land access. That means you need a leader with the nerve to face down any pressure from the State Department.