Making you the leader makes no sense. Having the mark on your hand doesn't mean you have the ability to be the kind of leader the Inquisition needs - its just an extremely fortuitous circumstance for them that you are so unusually amazing at everything. Putting you up there as a figurehead for the public is one thing, but they acutally *are* deferring to you and conferring that leadership role to you in private as well, which is just crazy. As several bright sparks point out, you don't even know how it works - you just wiggle your fingers and hey presto. How does that qualify you to be the Spearhead point of contact in all situations, chief diplomat on all critical matters (you use Josephine - your diplomat - for all the day to day stuff, but your Inqusitior handles all the important stuff without her?!)
The reality is that wouldn't work this way *at all*. As soon as they worked out that your mark was the only way to close the rifts, then that would be it for your personal freedom. You may be honored and valued by the Inquisition, but you would also be far too valuable and necessary an asset to ever leave to your own devices, even for just a few minutes. You'd be flanked by bodyguards and attendants everywhere you go - which wouldn't be far, because outside of pre-planned excursions to rift sites for closing them, you'd be confined to a place they can easily protect you. Because without you, they have *no means* of closing the rifts. They're not just going to let you go rolling about the countryside, with just a handful of people in hostile territory! They'd look like right lemons if the world was destroyed by the rifts, simply because they let you gallivant about, because you 'needed some space'.
Putting you into the role of leader is (as many have mentioned) just one of the many Disney like aspects of this game. To pull something like that off, the protagonist needs to be charming or charismatic or self effacing, hapless... something. But your character is just some tonally neutral avatar with a mark on their hand, with all the inspirational qualities of a dead badger. Instead of growing into the role, and as the OP suggests being presented with a trauma that *demands* you learn to overcome any doubts etc and knuckle down (which should be shown even if only in montage like in KOTOR), it goes thusly:
Advisors: So... we need you to be the Inquisitor.
You: Er... you want me?
Advisors: Yes.
You: Well... alright, then. (Spreads a map over the bonnet). We need to do this, and then I need all your intel on these people, then I'll lead these troops over here.... Come on people - I need options!
You're just instantly the most capable person ever at everything. And everyone else stops mattering at all, going back to their usual round of 'I've got trouble with my parents/parental substitute/old lovers' etc etc etc.Cassandra's fall from grace is simply the most pronounced, as she goes from Main Character to Yesterday's Hero. With absolutely no warning, she suddenly decides she has no interest at all in being involved in any of the big decisions, and that's that for her in the main story.
And what of Corypheus? Well, he's too busy sitting in his base thinking 'Man... why *did* I throw him right next to the last working Trebuchet, instead of just killing him?! And why did I tell him all that stutff about my powers and my evil plans when I was going to kill him anyway? Doh!'