The wisest of these analysts and historical spectators might be able to share with you an important observation about the Iranians. It's a human trait seen as a negative one by many but it serves the Iranians well. They hold a grudge and they never forget.
After the Iraq-Iran war, many were amazed at how quickly and swiftly Iran established ties with the regime that killed more than 1 million of its citizens; that included a considerable number of Iranians who lost friends and family in that war. It seemed like the hatchet had been buried to a point where when the coalition, led by the US, attacked Iraq with the obvious intention of not stopping until Iraq's military capabilities where devastated, Saddam trusted Iran with much of his riches and even airplanes.
Iran, of course, does not forget. Whatever Saddam smuggled and hid there became theirs in the name of war compensations. Iran even managed to cash in the American led toppling of Saddam in 2003 to its benefit; it now has the strongest armed militias in Iraq and a say in the actions of the Iraqi government.
Stating this serves as an example of how Iran does things.
Going back to the Iraq-Iran war, something had happened during that war which is not discussed much. When the Ayatollah took power after the revolution, he ensured showing support to Palestinians by giving them the premises of the vacated Israeli embassy. This was an unprecedented move. Shortly after, the PLO sided with the enemy and sent its Jihadists to fight alongside the Iraqi army against Iran. To add insult to the Iranian injury, Saddam gave a lot of the houses and properties confiscated from Shiite Iraqis to Palestinians who accepted gleefully; properties of Iraqis who were either deported or killed due to their Persian ancestry.
If we agree that Iranians do not forget, then they will not forget that Palestinians had failed the test of loyalty towards them and they would not forget that Israel, although very aggressive in its political rhetoric, has not physically attacked Iran. They might even not forget that when what seemed to be the whole world backing up Iraq in its aggression against them, Israel orchestrated "Operation Opera" which constituted a tremendous blow to the Iraqi confidence and feeling of superiority in its war against Iran.
Iran has no real physical conflict with Israel. What is happening in Gaza and Syria and possibly in the Iraqi Kurdistan region is fair game between Israel and Iran and their respective intelligence services. Neither country has actually assaulted the other directly on the other's territory. There are over 200,000 Persian Jews in Israel and another nearly 20,000 in Iran. Persia has an honorable history in siding with Jews and delivering them from Babylonian persecution. The Jews are grateful to this Iranian heritage; at least biblically.
There are so many reasons why Israel and Iran should be close allies. The reader would do good to differentiate between Arab and Moslem. Arabs have a historic quarrel with Israel while Moslems don't. Being Arab means you are driven by nationalism which does not accept the entity of Israel on their "cousin's" land but being Moslem means you cherish the people of the 3 holy books, it means you live in harmony with them and protect their place of worship like it was yours. This is, of course, the case with pure interpretation of the faith without the political and nationalistic tint adopted by hardliners who serve their earthly leaders before their divine one.
Iranians are Moslem and not Arabs.
One might think that an alliance with Iran is still not possible because Hezbollah is the archenemy of Israel and it is nothing less than Iran's long arm in the immediate region and that Syria is Iran's sister and it, also, is the most immediate danger on the other side of the border.
Regarding this, one should think hard about the situation Syria and Hezbollah are in. A situation of great disappointment with their Arab brothers. Syria has not just been abandoned by the most influential of Arabs, it has been subject to sabotage by them. It has lost faith in an all Arab united nation that is joined by language, religion, and blood ties. Syria is ripe for a change in its direction and all it needs is an Iranian path companion. Hezbollah is also constantly attacked by who are supposed to be the most enthusiastic about the cause, internally and externally. Hezbollah's ties with Palestinians are shaky at best. There is a confidence problem.
Silencing the politicians who instigate unnecessary animosity with their hate speech and constant threats would be a good first step. There is no doubt in the minds of friends or enemies about Israel's democracy when it comes to elections. The Israelis can bring about another Yitzhak Rabin who proved to be smooth on the ears of combatants on the opposite side. Then they can reach out to Iran and Syria who feel betrayed by so many of who should be natural allies. Love him or hate him, Assad proved to be intelligent and open to friendships. He has protected his minorities; a sign that shows he is very tolerant towards other religions and ethnic groups. Iran will appreciate the change in tone and will reciprocate all gestures two folds like they are known to do.
As for Hezbollah, they will follow mother Syria's and father Iran's wishes. Even more, they are an organization that may wish to prove its efficiency at peace like it did at war. Hezbollah comprises mainly the sons of the South of Lebanon and the Biqaa valley. They come from families that were fed up with paying protection money to militias, foreign and local. They are the sons of families who were forced to make financial contributions to combatants who used their land to launch attacks without their permission. If they are met with respect and good will, they will most likely listen to the organization's parents and make peace.
This is all wishful thinking of a man who loves humanity, a father who wants a better world for his children and a close spectator of Middle East events who has grown tired of seeing senseless hate and reprisal based on religious and nationalist considerations.