That would be the same misunderstanding Bush made. Iran's government is run by Mullahs, however they allowed more moderate and secular people to run the day to day affairs of government. The conservatives were losing ground to the moderates and it was the former's lucky day when Bush locked them into power. Now Mullahs do determine who can run for election and moderates do not exist. Clerics do have ultimate say, however that did not mean they had to run everything. They still delegate, but to people who never were for normalization of relations. Turns out neither were we.
The elected officials have no hard power. Like when Rouhani talked a little bit too much about corruption, the clerics told him to shut up and he did. If he really steps out of line they will do anything up to and including fabricating crimes to lock him away and replace him with someone who toes the line.
Similarly, media is very tightly regulated. Step out of line too much and you go to jail or worse.
Look at the Green Revolution and how the clerics tolerated it... by persecuting those involved.
The clerics especially Khamenei have ultimate hard power and control the security forces; Khamenei even has his own personal bodyguard and financial empire (some earned, a lot stolen, as I referenced above).
This is in addition to the patronage system that clerics and hardliners enjoy. There is grumbling especially among the young that one is too often hired and promoted based on perceived piety rather than ability, especially to higher government jobs.
Given how the Green Revolution failed, I am very doubtful that Iran will shake off the theocratic dictatorship, censorship, etc. anytime soon. I'm not even sure if they are really moderating all that quickly. Many of the people who hate it there leave for other countries, if they can, and conservative religious people make more children than the moderates. (A lot of times you meet some Iranians in the West and sure they seem fine, but that's a self-selecting sample. Iranians who are actually in Iran are on average more conservative. It's the liberal Iranians that are more likely to leave.)
If Iran does manage to replace the theocratic dictatorship with an actual Parliament or something, that could help a lot, especially if Iran stops sponsoring bad actors like Hezbollah and Hamas. If Assad is still in power by that time, he will lose his main financial benefactor and his regime would likely collapse.