Under the Shah, our "politicians" spoke not to the people, but in language that was meant to impress the Shah. That was because he was seen as the real "source" of power. Since none of the politicians owed their position to any popularity contest, none needed to impress the people. If they did become somewhat popular with at least some people, in fact, it might have even hurt their standing with the Shah (e.g. Prime Minister Amini).
After the revolution, even when we had reasonably fair and open presidential elections like the first elections that got Bani Sadr elected, the candidates who had the best chance of winning were those who had Khomeini's blessing. In other words, the formal process of "democracy" was established, but we were no closer to its real meaning. If Khomeini smiled at this candidate, his fortunes would immediately get a boost among the people. On the other hand, if someone like Admiral Madani, or some other figures, were seen not as close to Khomeini, the people didn't vote for them. That meant that while Bani Sadr might have imagined he got to be president because of the 'people', in truth he was elected because the people thought he was Khomeini's choice!
Khatami was our first genuinely popularly elected, democratic, president. Unfortunately, while his reform movement advanced the ball in many ways and has made Iran a much better society as a result, the regime decided to weaken the democratic institutions to offset the danger to it.
The issue now is how best to get the ball back into the court?
My judgment is that the best way to do so is to look for individuals whose power or fame come from their popularity. That will make them feel indebted to the people, and more careful not to lose their "popularity". Yes, Qalibaf is considered close to Khamenie, but he is a populist and has tried to sideline Khamenie's first choice (Larijani) by being more popular with voters than by being "closer" to Khamenie. I like to encourage that process.
In Moin's case, I like us to find ways to reverse the decision of the Guardians Council, without weakening the outlet that exists (however weak) for some forms of popular representation (i.e. the ballot box). In this process, I feel the best way to do so is the one I suggested, which is to protest this particular move and put pressure on this particular issue.
That said, I don't believe Moin would have won. Or that he was the right answer at this time. He would probably set the very reforms he wants to see take place, back. He is not trusted enough by the regime to even allow him some room to make incremental reforms, and he is not so popular to be able to either demand what Khatami couldn't or to even prevent a move to take him out completely.
The "balance of power" within the regime right now favors the conservatives, but these groups -- allowed to fight among each other -- aren't going to be able to stage a coup. Threatened enough, we might end up with the whole "democratic facade" put to an end. That would make some who like to throw slogans around happy, but it won't help Iran become democratic.
Instead, it would merely increase funding for exiled groups who want the US to fund their activities. It wouldn't even bring those folks to power, unless it is on the back of an American tank!
I believe Iran has a chance to become democratic in due course. But it won't, not even in the medium term, if the we make the wrong choices. At this stage, the wrong choice is to me would be encouraging what (regardless of our intentions) will lead to a divided nation that is thrown into civil war, disintegrates, and find a puppet regime to rule over what remains of it.