I suspect that was a result of cut content. No doubt the rise to becoming the Herald of Andraste was meant to be longer.
AS for the worshiping bit, notice that only those who don't really know the Inquisitor do so. Those who are in regular contact with the Inquisitor: Cassandra, Iron Bull, Sera, Krem, Vivienne, all see a person. One perhaps tapped by fate, the Maker, or whoever. But still an ordinary, flawed mortal.
They really don't. Look at how cheesy it was right after the Battle of Haven, when Cassandra goes, "the one who has been leading us all along" and Leliana holds out the sword Aragorn-Isildur style and then she climbs the stairway and the entire Skyhold apppauses while the golden light of a new sun shines in everyone's eyes and end-game-level victory music resounds. Pls
Then if you try to romance Cullen he's amazed like "oh maker, it's like banging Andraste herself" and Cassandra, in the Haven war room, goes "you were precisely who we needed, when we needed it" among other comments of superstitious reverence.
What did the Inquisitor even do before Skyhold? The Hinterlands? After 5 playthroughs I finally figured out that they were spreading the Inquisition's power through the Hinterlands, I guess, collecting blankets and ram meat, and killing....mages and templars, I guess? But Cassandra was the real force in Val Royeaux when they first met the Lord Seeker, and the advisors (particularly Josephine) set up that nobles/Templars meeting in Champions of the Just. The only accomplishment is that the inquisitor is able to escape the Envy demon in her mind. Although mostly due to Cole's help. In Hushed Whispers....honestly Dorian's the hero there. He knows about using the amulet to get back.
I get propping up a religious figure or celebrity to manipulate masses and forge political alliances. To utilize a marketing brand, of sorts, to create an image and garner a following. I actually LOVE that idea. The middle ages, a time when the majority of people were probably peasants, wanting to look up to prophets and heralds, and nobles manipulating that alongside a Catholic church. Um, didn't that kind of happen in reality? So yeah, I get it. The problem is, the game wasn't entirely self-aware on this. They merged a role of necessary agency with a position, as I just described, which only honestly works if it is a passive symbol. Like the Last Emperor. The Dowager and the advisers were the real rulers of ancient China. The little baby Emperor is just a symbol, that has multiple uses, and meanings, to the public at large. But he's just a baby. A better protagonist would have been an advisor. Who doesn't necessarily receive the worship on a national scale but gets to kick as* and, probably determine the fate of the nation. Individual groups and people may praise him, like when the new keeper thanks the warden (after a legit boss fight), the king of Orzammar, Bann Teagan thanks the warden. But then they move on.
Being both the symbol and the active agent of change could have worked, I suppose, if we directly controlled more operations on the field instead of just 3 companions.