OP's spot on.
The favoritism becomes even more blatant with how the writers retcon, whitewash, backtrack and blackwash to try and hold up the Chantry on a platter higher than other faiths.
1) In-game, Alistair speculates that Templar abilities do not require lyrium and that lyrium is just a means of control by the Chantry. Speculation supported by how Alistair and the Warden can use templar powers without lyrium and leaves us thinking about what templar abilities truly are and whether they qualify as magic.
But Gaider retconned Alistair and turned him into a liar by strictly confirm that lyrium is necessary for Templar powers. Which basically infers that Alistair was lying and taking lyrium behind your back or that this part of the conversation never happened. But then in Inquisition, the writers contradict themselves when Cullen confirms that templars don't start taking lyrium until after they complete their vows and Alistair was recruited before his training and yet could still use templar powers despite not taking that first draught of lyrium. Sloppy writing? Lack of narrative coherence maintenance? Or blatant backtracking which results in more potential plot holes?
2) The Dalish system was not portrayed as better or worst than the Chantry system, just different. However, once two games confirm that the Chantry approach to magic is objectively problematic and makes more problems than it solved, it looks like the writers realized that other magic systems like the Dalish seemed far better by comparison. So instead of acknowledging this fact and working it into the story, the writers throw in a bullshit "three mage" rule for the sake of knocking down and blackwashing the Dalish to try and make the Chantry seem better.
However, this still fails due to the fact that the Dalish don't view magic as a corrupting influence, merely as a natural part of the world. Therefore, they appear to view magic with healthy respect and caution rather than dogmatic suppression and fear like Andrastians do. And the Dalish viewpoint of magic didn't result in a continent-spanning war that brought their civilization and system of faith to the brink of destruction. Which makes the "three mage" rule retcon and other slaps in the face to the Dalish all the more obvious as intentional or unintentional incidents of black-washing.
3) The noteworthy absence of City elves and the lack of reference to their plight also seems like a deliberate exclusion to whitewash the Chantry. Not only to keep things PC, but to also keep from reminding the players that there's an entire caste of people whom are oppressed, tormented and abused and the Chantry either looks the other way or condones it. Oh wait! It was the Chantry who ordered the alienages to be set up in the first place. Places of fervent poverty where people are barred from livable work and the right to defend themselves; hunger and crime are ripe; and elves are often murdered, beaten, raped or sold into slavery without consequence. All under the Chantry's loving watch even though these people are supposed to be followers of the faith as well. This horrific reality of life was forced on city elves as the gift for renouncing their false Dalish beliefs. Yeah, great trade or wait, it's not like the elves truly had a choice what with the Chantry and Orlais completely stripping the elves of the homeland which Andraste's sons gave to them in gratitude for the aid which Shartan and other elves gave their mother.
And to add insult to injury, Shartan's deeds were rendered as heresy and banned from the Chant. Even though Shartan and his followers died protecting Andraste. Go ahead and defend this one Bioware, I'll wait. And the "flawed and human" excuse won't work here or anywhere else.
With that in mind, it's unsurprising that the Inquisitor can't be a City elf. After all, can you honestly see a City Elf Inquisitor being able to sit in the same room as Celene, knowing that the empress ordered the deaths of thousands of elves? Or that Celene leads a nation where thousands of elves are crammed into a small living space inside of Orlais' capital that's barely the size of Denerem's market square? Or that Orlais' celebrated Chevaliers have a graduation ritual that involves slaughtering elves to "test their blades"? Or the fact that according to the History of Ferelden codex, Ferelden elves were sold as property by Orlesians during the Occupation? And how does this reflect on the Chantry that not only is Orlais the empire that formally organized the Chantry, but that Orlais remains the nation that's closest to the Chantry?
But no, none of the above is hardly mentioned or shown because that would make things uncomfortable and weaken any defense of the Chantry that the writers or Chantry supporters could try and come up with.
4) Deliberate side-stepping away from true criticism and questioning of Chantry beliefs and Andrastianism which the OP already spoke of in good detail so I won't be redundant here. I will say that the PC is allowed to discuss related matters here, but the game locks the conversation from being too critical of the Chantry and ultimately, the PC is forced to be an Andrastianist ally despite being held as a demi-god himself and could easily have the power and pull to either take control of the Chantry himself (per the dropped Inquisitor Divine ending) or become the founder of a new Andrastian Faith that's closer to Andraste's teachings in practice and writing than the Chantry itself.