So if you say that the reason this ignited was because Egypt allowed it to happen, isn't this saying that either, bribery took place, or Israel's neighbors are not ideologically aligned with Israel, or a combination of both, i.e, mutual incentives for an ideologically aligned bloc?

Saying that Israel needs to do x, y, z is just ignoring the fact that it didn't do that then, and that in the future it won't be able to control all of its neighboring states. It'll be some other proxy war. Israeli government can't change the surrounding world just because it wishes to. At some point, Gaza might be long gone, but in order to achieve that, Israeli government will heighten the hatred of those nations in the world that are opposed to the Israeli government.

No? I don't think the demise of Gaza is the end of the problem.