And the real antagonist in DA:I is arguably Solas. Which, I admit, does make that plot thread of DA:I feel a bit inconsequential, like a very long set-up for something that DA4's hero gets to solve. I think the reason that DA:I feels lighter (if you don't include Trespasser) especially in your downtime at Skyhold is not any one detail, but that the story progression was off. Corypheus only was a threat up until the attack on Haven. Urgency was necessarily drained by hours upon hours of open-world questing afterwards. To restore it, the Temple of Mythal and the final boss battle should probably have been combined, as has been suggested before. The Inquisitor also has a position of immense power, with a big castle, armies, etc. You also had armies at your call in DA:O, but I found the mood there more intensly hopeless because what you came back to was a camp with like ten people around a little fireplace in the dirt that you accessed by clicking on a map that was slowly burning up behind you.
However, the Inquisition was also there to put a new Divine on the Throne and generally restore order when the world was literally falling apart. For me, I never really thought about Corypheus' much (which is a writing failure), but then again, it's not like the Archdemon was that much more compelling. DA:I was more about establishing a presence that had the power to keep the Mage-Templar war from escalating further, make Orlais a halfway stable country and generally clean up. It's very different from DA:O, but if I want to play DA:O, I'm gonna play DA:O (and the truth is, I rarely want to play DA:O because the combat is like pulling teeth).
And brothels? Where would we have had a brothel here? Redcliffe and Haven are too small, we only saw the nobles' district of Val Royeaux and the Inquisition is half a Chantry operation. I think forcing a brothel into any of these places for the sake of having one would have felt more juvenile than mature.
And I know, this is about the dreaded PC crowd that has been TEARING OUR GAMING WORLD APART (read: groups that aren't me are being catered to and I don't like that), but it's not like there's no heavy themes in DA:I. Iron Bull is lugging around a whole subplot of torture-reeducation (not to mention there's some indication he saved Krem from being raped, if you listen to Cole), there's plenty of death and murder to go around for everyone both off- and on-screen, we have the mayor drowning refugees, lots of codex entries with creepy diaries and letters, the world ending in the mage storyline and a whole Order mutated into monsters in the Templar version. Then there was just exploring areas: the desolate nothing of the Hissing Waste, the burning pits with bodies in war-torn Orlais, the swamplands filled with skeletons and other remains of last survivors. It's not as in-your-face as the DA:O City Elf origin, but then again, I always find that level of forced darkness a little grating. I find an atmosphere of suppression and dread, like many areas provided for me, much more effective than rape and graphic violence all over the place.
I think it also helps that Orlais plays a huge role as far as setting goes, and the urban parts of Orlais lean more towards Sun-God-Era France than your usual medieval fantasy stuff, thank the Maker for that. I don't always need to follow characters through versions of medieval middle Europe/England. However, that gritty medieval fantasy setting makes brutality more immediately obvious, whereas it hides behind masks and pretty facades in Orlais.
Really, I think the issue is that the games are all different because Bioware has always experimented with storytelling. DA:O is your standard dark-ish fantasy fare of Hero saves the world; DA2 tried to do a more focused story with a frame narrative and a structure like a fantasy trilogy, with three separate climaxes focused on one person; DA:I doesn't have a strong focus on the ending, but is a more 'the road is the goal' idea of building up an organisation that prevents southern Thedas from falling into chaos until some more stable structures are re-erected so we can then move on up North for DA4. All of them succeeded and failed in some ways and I think it's fair to like any one of them more than the others, but as 10 pages of discussion show, no, obviously none of them is objectively better than the others.