I don't think omitting the older generations of consoles would've made that much of a difference, honestly. As others have pointed out, much of DA:I's problems go a lot deeper than what could've been solvable by skipping a generation. For another, even as it is now, somehow they've managed to make the game run like a potato even on a decent machine. I can run W3 maxed out except for hair works and barely ever dip below 60fps. If I start playing DA:I, soon as you get too many NPCs on the screen, bam, you get drops. And let's not mention the choppy mess of cutscenes, which you can "fix" by forcing the engine to render them past their soft-FPS cap of 30 if you're willing to deal with weird, crunchy audio. And random scenes where slowdowns just occur, always, for no apparent reason (Varric asking Quizzie if they should have a party after recruiting mages/templars is one that comes to mind immediately).
DA:I needed another good 6 months in developement. Instead we got ANOTHER pointlessly tacked-on multiplayer component. Which, probably, some people play, somewhere. I guess?
Trespasser is structurally what the rest of the game should've felt like. And sure, we could have had some large areas to roam. But collecting **** and fixed conversations should not have been the bulk of the game.
Don't get me wrong, I've sunk hundreds of hours into DA:I. It has the core of a good game. If only Bioware had taken the time to iron out the clunky mechanics and pacing issues they KNEW going in that the modding community wouldn't be able to fix, we would all have gotten a better experience, and many people would not be in the situation where they're starting to doubt where the devs are taking the series. And also worrying about ME:A.
PS3 and X360 compatibility are only a very small part of the problem. My money on why certain things were scaled down (like Val Royaux, cutscenes in general, the whole cut plot line about defending Skyhold, etc) is that they simply couldn't figure out how to implement these things properly in Frostbite without going either stupidly over budget or past deadline. So they filled the world with little quests and called it a day. Little quests without cutscenes, because every added cutscene appears to be tied/synced to sound and music somehow, and any variation in FPS tends to make the game want to sh*t itself. Add in multiple platforms to that, and it gets nightmarish to develop.
tl;dr: I think porting to older gen probably didn't help, but DA:I was doomed to be a disappointment from the start. I think they just bit off more than they could chew.