First, there are TONS OF SPOILERS in this post. Reader beware!
There is one key area in which DA2 fell short: Hawke's inability to impact the world around him (I'll be using a male pronoun for Hawke in this since played a male 3/4 times). Don't get me wrong: there are a number of times in which your character's actions have meaning, but all too often not in the "right place." What do I mean by "right place?" Well, I mean in matters of significant overarching story and plot development. While it's great to see how your lack of relationship building affects how your Companions treat you (particularly in the Last Straw), that's not nearly enough and it's the place where DA2 falters.
Now, let me be clear here: I love DA2. I've played it four times in a row and I intend on playing it two more times to experience different classes and romances. I've bought and played Legacy 3.3 times. I am a Bioware fan, having played the BG franchise and other games that used the Infinity engine. I am not a PC "elitist" (whatever that means), but I do consider myself an RPGer. So, do not presume that I'm bashing the game; rather, I'm throwing out areas in which Bioware/EA could have granted you greater influence on one's game experience. Thusly, my nine thoughts:
1. Hawke Sibling's Death: There is NO reason why either of your siblings had to die. The argument I heard most often for this was class/party balance and I cry BS. With three Hawke kids and three classes, you had a perfect little trifecta (not using the word right, but you get the point). If you played a mage, then Carver was either a warrior or a rogue, and Bethany took the difference. Or the game assigned the classes for you. Now, your choices in Lothering could/should have impacted whether the ENTIRE family made it out alive. Throwing in a couple extra scenes that show you picking up Aveline or not would have been a starting place (for example, deciding to avoid the Ogre but taking a longer way around with less access to loot) And these are just a variety of ideas. As an aside, surviving siblings can still become Wardens, Templars, or Circle Mages.
2. Bloodmage Reaction: No one ever notices that you're a bloodmage. Ever. While most critics of the game harp on your being a mage going ignored at some of the strangest times, aside from Cullen inexplicably not noticing, the game makes some effort to acknowledge why the Templars give Hawke a pass. But, as a bloodmage, your Companions should have some idea. In particular, Fenris, Anders, and Merrill should have a conversation with you that has huge implications for your Friendship or Rivalry (F/R). Hell, if you don't answer questions to their satisfaction, Anders or Fenris might even leave you regardless of how strong your relationship is with them.
3. Restricted Party Interactions: Let me offer a caveat here before getting into it: I like the conversations in this game a little more than those in DAO. They tended to be deeper and more closely tied to your F/R. However, I regret that they occur in such a spread out fashion. There should have been more opportunities to initiate converstaion in the Companion's base. Keep the Quest option for big conversations, but allow a few player initiated, "more mundane" conversations opportunities to occur. In short, Hawke goes out of his way to follow-up with his friends. This also gets a little bit into the whole three year gap business. Most of the more meaningful events occured during these times. Hawke initiated conversations would allow those Codex entries to seem more organic and less like a dull biography.
4. Templar vs. Mage Support: There should be a moment in which your decisions in the first act influence which faction comes to you for a wider variety of sidequests. You sort of get this based upon how you treat with the Starkhaven Mages, but it's not really enough. You need a greater role as a Templar agent or Mage supporter. You need to meet directly with movers-and-shakers in the Second Act (particularly Orsino) so you can get a feel for what's truly at stake. This would reinforce that this sociopolitical issue is the game's driving narrative much, much sooner, and you would have a greater role to play in the final battles. How badly a Mage supporter impacts Templar reputations and numbers should have resulted in different cut scenes during the Last Straw at the Circle with many more Templars going down; conversely, the reverse would occur in a Templar agent Hawke. This sort of change would be especially key in how the next element is handled:
5. Anders: If you're Ander's friend or in a romance with him and you take the time to really, truly help him, you should have had the ability to talk him out of blowing up the Chantry. Hell, if you did a really great job, there could have been a special quest that really allows him to be freed from Justice. The Chantry could still be destroyed (I would argue "has to be"), but with the inclusion of other prominent mage NPCs (of which there's a dearth), one of them could have carried through on what Anders planned. This way, you influence precisely what happens with someone whom you trust and/or love which gives you as a player a greater sense of influence and achievement, and your Hawke greater claim to a Champion with agency.
6. Orsino: For me, this was the absolutely dumbest boss fight in the game in a Mage-supporter run. When Orsino gives into despair and becomes an abomination, I was pissed not because I liked him (didn't get to know him enough to like him... see #4), but because I should have had the opportunity to sway his decision. And I should have gotten experience for it (see below). If I played the game in a way that showed I was capable of supporting Mages without resorting to blood magic and/or brutality, or if I had high enough Persuasion (yes, skills like this should definitely come back; see below), I should have been able to talk him down. If Orsino's later killed by a Templar assassin or by Meredith, fine, but at least I can say that my actions determined how the end game pans out. The only time Orsino should be an enemy is if you side with Meredith. At that point, he turns into an abomination (and I would argue that you should be able to talk him out of that if you make it clear that you don't support the Right of Annullment, wich would then turn Meredith against you). Speaking of Meredith...
7. Meredith: More of the same. If they wanted to show how crazy she was, they did a bad job of it. Her paranoia should have been more obvious in the Second Act. Her occasional bouts of sympathy for the Mages makes her paranoia seem out-of-place. That having been said, like Orsino, you should have been able to talk her down from attacking you. In essence, the final boss is determined by your choices, your influence, and your actions. Yes, someone could still fight BOTH Orsino and Meredith, but it shouldn't be a given.
8. Experience for Story-Driven Influence: If I manage to talk someone out of some action that would otherwise result in combat, I should receive commensurate experience. This sort of thing would encourage a greater RPG sort of play. Elements along these lines are what made Planescape: Torment one of the best RPGs that used the Infinity Engine out there: your dialogue and ability to interact well with others (often requiring decent Intelligence, Wisdom, and/or Charisma) drove the story as much, if not more than, your physical abilities.
9. Reintroduce RPG Skills: I don't know how many people didn't use skills in DAO, but for me, such sklills are a given. As a result, make taking them have a real impact on abilities or something. Or don't. Not everyone is going to play a silver-tongued diplomat or intimidating brute, but the option should be there beyond just one's tone.
So, those are my ideas of what DA2 could have done to ensure greater agency and player impact. You'll notice that I didn't mention things like Mama-Hawke's death. Well, there are and should be some things your Hawke can't always do. Something like your mother's murder in a game in which you have had real influence and impact would really resonate. Unfortunately, while I hated that she died, all it did was reinforce how limited my decisions were despite being a noble and, eventually, Champion. It's these kinds of things, IMO, that should be incorporated into DA3. Although I know that I'll eventually have a boss fight, I should feel that I influences how that fight occurs within a living, breathing game. The inclusion of more such elements would have made a good to great game a spectacular game.