Regime and instutional change like this simply does not work. Adopting a mindset of 'If we just remove the bad people, and put nice people in charge who seem to support the right agendas, everything will be okay' has failed again and again and again and again the world over, throughout history. It inevitably leads to collapse and period of rebuilding, where some kind of compromise has to be re-established. Because you can't just impose ideology, it has to be sea change over time, achieved by constant campaigning, and education to tell people *why* it would be a good thing to adopt your reforms, and how you planned to do it.
Simply saying that people are free and should co-exist, because that's the right thing to do, has no currency whatsoever. Look at the issue with Elves and their presence in human society. They are firmly segregated, by mutual choice (Kirkwall's Alienage has a note explaining that the elves don't actually have to live there, but when they do try to settle outside the Alienage, humans burn down their houses and attack them). In Denerim, elven rights are at the back of the queue in terms of Anora's agenda, and manages to get pushed even further back during the Blight when her Father tries to sell them all into slavery, because as he explains 'Its not like they have any kind of decent life here, is it?' The fact is that most people see Elves as little more than vermin, scurrying about getting into trouble and taking up space. There is no dialogue between the races for the most part, and the path to there being such understanding will be long and difficult. So yes, reform is necessary and race relations certainly need to be higher up the agenda, but you can't just clap your hands and say 'From now on, the Elves and humans are friends - because I'm the boss and I say so!' and expect things to be any different. Not unless you're willing to adopt the Qunari philosophy anyway.
People fear mages, they think and have been taught and have seen that mages bring trouble, are trouble and go looking for trouble in all kinds of ways that the common man thinks only crazy people would do. Varric is mostly of this opinion, and he's about as laid back and liberal as you can get. He's willing to take people as he finds them, but admits that mages are often dangerous and go messing about with stuff that no right minded person would ever think of. So if even Varric has issues with them, how do you think the hard working, hard drinking man on the street is going to feel if he's suddenly told that mages are completely free to mingle and live amongst them? After the sky has just been ripped open and an army of mages tried to kill them all? Shortly after a mage uprising with chantries destroyed etc etc? There is no real understanding of mages, beyond the general feeling that its all unnatural dangerous business that decent folk need to be avoid. You will only change people's minds through education, measured integration of mages into society and through positive role models working to improve people's understanding. And even then it will takes decades at best before things really start to improve. There are no silver bullets for things like this.
Reform does need to come, but the people can only take so much strain. After everything they have been through, they want peace and normality for a while, with no wars, no riots, no factions tearing at other in political or racial squabbles. Changing everything they believed in, and bringing in radical reforms that will inflame tensions from the highest pillars to the grass roots levels, is not going to achieve anything like that. It'll lead to chaos, as the Chantry and the followers of the faith in general splinter in factions and protest groups. And amongst those who know of her, Leliana will never be accepted as Divine. Justinia had a hard time finding acceptance because of her background - Leliana is practically a celebrity amongst the nobles of Orlais, with a very specific and ominous reputation. And if she is acting like Mafia boss Murder Pope, that's even more ridiculous.
Bioware are serial offenders at over simpliying complex issues. Remember Mass Effect 3, and the Genophage? Where you could support the Krogan (who had not 1 but 2 fan favorite characters supporting them, along with the much hyped Krogan female Eve and who practically had the ME team standing behind them cheering whenever they were on screen) or the Salarians... who had some pantomime villain of an old crone who was auditioning for Nastiest Person Who Ever Lived, and who you could almost hear 'BOOO! HISSSS!; every time she spat something at you.