Hrm, I'm going to make a list of what I'd love to see in a perfect world, with the understanding that it might not be feasible to implement some of the things I'd like.
1. Since exploration will likely be a component of the next game as well, create better developed zones that have a central story arc where most of the sidequests in the region connect to that central story arc and the central story has more than one way it can be resolved. For example, if there were competing factions in the area and you could only ally with one, changing what sidequests you had access to. This would increase replayability + add for more chances for you to define your character. I believe this was the original plan for DA:I and a large criticism of it, so I think this is likely to happen in DA4. At least one large region should be an explorable city. Ideally, two explorable cities, each supporting one side of a geopolitical conflict we'll be navigating.
2. Continued support for multiple races + better integration of their unique backgrounds, abilities, and social standing. This could include certain parts of the game where each race has more complex ways of dealing with a problem or more obvious investment in it, as long as it was well balanced so that no PT's experience feels more meaningful.
3. More opportunities for the player to develop their characters background + have the game remember it and reference it later. (As flavor for developing and roleplaying characters, not impacting the story. This wouldn't have to be in depth, just a few nicely placed references)
4. Deeper interaction with companions. Companions often spend a lot of their early word budget explaining parts of the world to the player. Instead of this, find early mandatory quests that show the player the world, then let the interactions between the player and their companion's investigative dialogues be more about processing information through debate and discussion. A lot of consideration should go into the range of expression we are allowed to have when reacting to companion's statements, particularly ones that involve strong opinions. Companions should be allowed to have radical opinions or ones that radically diverge from ours, and we should be allowed to respond to them from several different viewpoints, such as agreement, partial agreement, bringing up supporting evidence if applicable, agreeing to disagree, or definitively stating we disagree and will work against them. In turn, companions should call us out if we express one thing to them as our stated goal, but then act against that goal with our choices.
5. Better integration of story arcs in the political sphere. For all the lip service to how complex and political the Orlesian Game is, in execution it was disappointing, but the idea behind Wicked Eyes, Wicked Hearts - that an important part of the game can use discovery/intrigue/dialogue options instead of combat - is exciting and deserves more work. The Landsmeet was a starting point, WEWH built on it + the war table mechanic offers more opportunities to develop it, now deliver it in its full glory.
6. Use the opportunity of it being set in a place far away from the events of the past three games to distance it from the complications of the past three characters actions. Less returning characters = more chances to use those characters meaningfully or successfully when reflecting on the past. If that means the only way I can see Fenris, a favorite of mine, is if I choose to return him to Danarius (something I could never do), so be it.
7. If the Qunari-Tevinter issues are to be a big part of the story, then let us have a window into how these issues affect regular people living under the Qun and under Tevinter rule. Flesh both sides out so that it's not an easy situation, but don't fully demonize the systems they live under or present both as societies full of good people with very bad rulers. Show us a diversity of opinions within each group and allow us to side with or disagree with certain subgroups.
8. I really enjoyed dialogue perks and would love to see them further refined. Ideas for this include characters automatically being assigned perks based on their backgrounds (for example, if Inquisition, mages having Arcane Knowledge, Cadash having Underworld, etc), or the player being limited in how many perks they can pick in one PT. Perhaps you gain perks through completing certain quests, acquiring certain agents, etc. Or perhaps at certain points in the game you're asked what area of research you'd like to prioritize, and then you gain perks that way. Basically I think it'd be cool if they were integrated more into story choices and were more limited, so you had to choose which areas your character grew in.
9. Tactical cam is a neat idea, but needs more work to be functional. Refine this, or bring back more advanced tactics, or both.
10. Improved war table. I don't know if it will be called a war table in this game, but I assume a similiar concept will be in place in the next game. It's a great way to add flavor and additional content while bypassing resource issues. A lot of the war table missions in DA:I were not that interesting though, tbh, so the player was not really incentivized to consider them carefully. Having more war table missions connected to the character's background, class, specialization, etc would be a great way to add content without taking up a lot of resources, however, any consequences to those missions that have enormous implications (like Lavellan's clan) should be addressed in game quickly or perhaps not even exist.
Then I have a list of things that I would prefer for myself, but aren't as "I think this would improve the game for everyone overall". 
1. The fate of drunk!Alistair. I need to know, okay! Could be a brief mention on the war table, or I suppose he could show up if there was a way to do it, but...I just want this.
2. Dwarf romance
3. What the heck is the Architect doing, if alive.
4. More dwarf lore.
5. No on-screen appearance of the Inquisitor (or other past PCs) unless they are playable, especially if they are dealing with Solas, and this is introduced in a way that makes sense and doesn't detract from the current PC, who should be the focus.