You forgot that in the 80's when Iran (recently established Islamic Republic of) was invaded by a coalition of 30+ countries it was Hafez Assad who helped Iran greatly. In fact one of the reasons Iranians helped Bashar's Syria in the 2000's was because of the Hafez's Syrian help in the 1980's.

The relations are also a lot more complicated than it can be explained in one sentence like you did here.
For example you say "Iraq after Saddam" but you are also forgetting the Badr Army (Iraqis who fought for Iran against Saddam's invasion of Iran).

You see, rulers come and go. The worst of them go sooner than others. But the people of the entire region (West Asia) share thousands of years of history, culture and are from the same ancient civilization even if some have forgotten it in the modern days.

Saddam's aggression toward Iran was due to his delusions. He thought he could become leader of the Arab world while in Iraq the Ba'athi regime was a minority that wanted to rule over a majority (various ethnic groups) none of which wanted them. So in order to rule over them, he needed this find common ground and he thought there is nothing better than inventing a foreign enemy.

But since such "bad relations" are not natural, they don't fully work. This is why we see Badr army, this is why we see Iraqi Kurds that don't cooperate with Saddam to the point that he drops chemical bombs on them, and so on. This is why when Saddam is removed, the relations between Iran and Iraq goes back to normal.

This is also why I believe despite the dark days ahead of Syria, the end result is going to be good. Turkey is now seen as a pariah state. And despite what the propaganda may say, people are going to see the difference that The Resistance made in Syria liberating the entire NATO-backed-terrorist occupied territories about a decade ago.
This is why everyone is predicting how The Resistance is going to grow in the coming years.