Ancient Egypt ruled up and down the Levant. The Persians/Babylonians (Iran) held all the way to Egypt. The Syrians (Assyrians) held it. And the Romans did, and Atilla the Hun did too.
Some irony in that this region is still so important. During the Bronze age (apx 3000-5000 years ago) there was no empire but a lot of trade. The most important trade to the countries, for their armies, was Copper and Tin which when smelted together made the bronze swords and shields and armor. Copper came mostly from Cyprus and Tin from Afghanistan areas. Later, spices, foods, wool & cotton, gold & silver, livestock etc all traded. If you know your geography you know that the trade routes naturally ended up with the Levant (now Israel mostly) being a sort of central hub.
There were no real empires (as we think of them now) in the Bronze age. You just had a lot of trade. From the Berbers (Morocco) to the Hittites (Syria) to the Greeks - all around the Mediterranean - they traded goods and prospered. There were of course wars. We know the ancient Greeks and Spartans were independent confederations not really a cohesive political leadership. And we know that various tribes made allied treaties of defense and conquest. But for the most part this region flourished through trade.
Today, religious and ethnic tribalism plays a bigger part. The Turks hate the Armenians and Kurds, and fear they will lose land to a Kurdish state. The Shia and the Sunni war over what we would consider small religious disputes like praying at grave sites and lighting candles (which, ironically, the Israelites also argued about which is why some groups moved to the desert and we found their dead sea scrolls listing their greivances).
But for the life of me I don't know what business Saudi Arabia has installing troops in Syria. Ostensibly to support the Kurds. And maybe we see something of Trumps "deal of the century" revealing itself. He wants a big peace plan to encompass the whole enchilada falafel, from Israel-Palestinian to Kurds to who knows how far reaching it will be.
Like many I am astonished that the left is reacting negatively to troop withdrawals. This is what they elected Obama to do. Instead Obama mucked it all up with his regime change and Iranian sycophancy. We should be out of Syria and the smart player he is Trump slow rolled his plan to embarrass his opponents. They cried about pulling troops out of Syria and now we know his plan is bigger than the day to day announcements. These people hate Trump so much they just rail against him no matter what. They give him zero credit and I can list many things they should have given him much kudos for doing.
Anyway, let's see how it plays out. Mattis, at Trump's orders, gave the Saudis a 30 day deadline for cease fire in Yemen. That war is a huge mess btw, so he is right imo. Yemen doesn't matter. Iran is going to get distracted elsewhere now and besides, a pro-Iran government in Yemen that is not openly hostile is not the top priority.
I have some thoughts on how things might be proposed in his "deal of the century" but don't want to jump the gun. Let's see how it shakes out. One thing for sure, Trump 2020 re-election campaign is underway and imo he is finally starting to make the right moves (again).
I agree with our President that we should disengage and choose different methods to influence that region.
You are incorrect about Yemen: control of Yemen means control of the Suez Canal - which means the main supply line to Europe is severed - and brackets the Saudis and Egypt. Iran knows what it has been doing and we have to help find some way to solve this. The Saudis have been doing a horrible job of it.