That would be an incredibly bad idea, even if were feasible. The reason that Israel is currently so against an independent Palestinian state in area A is because of the lessons of the Gaza withdrawal. in 2005 Israel uprooted 8k+ Israelis who were living in Israeli towns in Gaza. They left behind all their infrastructure, including millions of dollars worth of greenhouses and agricultural equipment. The whole idea was that if the Israelis left Gaza, there would be less violence in Gaza, and the Gazans would stop shooting rockets from Gaza into southern Israel. That plan failed miserably. All of the infrastructure the Israelis left behind was burned or otherwise destroyed in massive riots celebrating Israel's withdrawal (pretending it was a great Palestinian victory). Then, Hamas won the first and only election in Gaza, and used that as the excuse they needed to take over the entire strip in a coup. After that, the number of rocket attacks against Israel increased dramatically. As a result of the massive increase in rocket attacks, Israel has been forced to fight three full scale wars against the Gaza strip. They have refused to invade and occupy it again, because it would cost far to many lives to be worth it to the Israelis, and would probably only slow down the rate of rockets rather than stop them (since when Israel did occupy Gaza, there were still lots of rockets being fired at Israeli towns).
In other words, The Israelis gave the Palestinians a proto-state in 2005, and in return they received thousands of rockets a year which cost them three wars in a decade, and now Gaza is too expensive to retake in terms of lives, money, and political capital (both domestic and international). If Area A became another proto-state, it is highly likely a similar situation would develop. Only instead of raining rockets on the relatively sparsely populated Negev (where Iron Dome is highly effective and efficient), an Area A state would be able to bombard the entire Israeli heartland from Jerusalem to Tel Aviv on a daily basis. And again, in such a circumstance it would be too expensive in terms of lives, money and political capital to reoccupy the area after the Israelis beat whatever conventional forces the Palestinian state was able to muster. Using Iron Dome and other active defenses are at best an extremely expensive stop-gap measure in such circumstances. The Palestinians can afford to build more Kassam rockets for $100 than the Israelis can afford to fire $70,000 interceptors to stop them. That is why the Israelis are leery at best about a Palestinian state. They don't want a second Gaza in a much more dangerous position on yet another of their borders.
The last thing the Israelis want is a completely lawless territory on their border, because such places tend to get taken over by groups like Hamas, ISIS or Al-Queda, and having Hamas to the South and Hezbollah to the North is bad enough. They can't afford to dismantle the PA in a war without reoccupying the whole region for fear of a new ISIS or Hamas controlled government taking power there.