DA:O and DA2 explored the risks mages pose when pressed, desperate, and driven (the Broken Circle in DA:O, and Blood Magic/Possession in Kirkwall in response to the Gallows system). Hence the presence, and then over representation in DA2, of abominations (which literally rose up from the ground in DA2, making zero sense). It made sense to have Abominations because the "dangers of magic" being explored in both games was isolated largely to the "mages" plot lines.
DA:I explores the dangers of a magical world. Corypheus, the Seekers, the Templars, the Rebel Mages, Elven Scrap Metal, and the Wardens. No longer was the plot of "magic is dangerous" isolated to those born with magic, but expanded to those who use non-intrinsic forms of magic like the Red Templars.
Abominations are best used as a plot device in personalized, built up, and highly emotional moments, which DAI did not have an abundance of. Having abominations in DAI would either get overshadowed by Red Templars (who are basically abominations) or would have become gratuitous like Red Templars/Venatori in DAI or when abominations would rise up out of the ground in DA2. Which would have been a shame.
Also, from a game mechanic perspective, what is the functional difference between fighting an abomination and some of the templar mooks? Than some of the demon types? It would have been more repetition in an already repetitious game.