I do not mean this to be rude, so I hope no one takes it the wrong way. Why must the Orthodox seek approval from the secular government of Israel to elect the Patriarch? This seems like a holdover from Byzantine times when the Emperor was a Christian or maybe Ottoman times when the Church was beholden to the Turks. Why should the Church give Israel's government a say in who the Church chooses to be its leader? Is this true in other places? Can the Ankara government veto the Church's choice for the Patriarch of Constantinople? Is this true in Moscow, etc.? Just wondering.
Linus7 is right, you are not being rude. Good questions all.
I THINK as far as the old Byzantine Sees go, it's a matter of old canon law. But the reality today is control of vast church real estate holdings in both Turkey and Jerusalem. Re-defining these relationships may put in question things such as the Jerusalem Patriarch's legal ownership claims to most the best of (east) Jerusalem which he has had for about 1500 years.
The Church is still under the Turks' thumb; yes they can withhold approval and the new patriarch can not "transact" legally. Same in Israel. Antioch (now in Damascus) gets approval but does not have the asset problem to the same degree; ditto Alexandria.
Don't know about Moscow; but they've got their own historical woes with the "State".