and when one of the citizens of this new state decides to lob mortar shells over the new border, Israel will have Causus belli for an actual war against the new state.
Not really. In the world, states are not considered responsible for private persons deeds. Israel also doesn´t launch a war on itself when an Israeli citizen commits a crime.
Actually that's the whole purpose of an international border, and in most cases the citizens of a country aren't crazy enough to start shelling their neighbors. A government is responsible for the actions of its citizens if they decide to attack across an international border.
The government is in duty to forestall such attacks. But it is not responsible for the attacks, as long as it doesn´t order or tolerate them. The attacked state, on the other hand, is in duty to refrain from actions that make people that angry that they make rockets and fire them at it.
Nice attempt, but fail. If any government is unable to control its border in such a way as to prevent its citizens from shelling a neighboring State, it is not fit to govern.
It also has to catch and punish any citizens that do it, or the neighboring country is 100% justified to protect itself as it sees fit.