In ME3's case, there was a certain novelty to just playing as a geth or asari, given that the protagonist in the singleplayer was limited to Shepard. Anecdotally people had fun roleplaying as a team of krogan warriors avenging Tuchanka or whatever.
Not to mention that they could do more story-based missions like SWTOR's flashpoints or (I think it was) Neverwinter Nights' co-op campaigns.
That is good strength of design, because it was a by-product of the mechanics presented through multiplayer.
If BioWare is smart, they would do some research and see what people did while in the trenches during Galaxy at War. Contextually the mode fitted into what Mass Effect was doing.The problem with games like Titanfall, for example, is that it has little to no context of the reasons "why" the fighting is occurring. Even in the story mode, which is of itself in the background and done through comm chatter and the like, is thinly veiled to service a reason for pew-pewing.
There was missions behind Mass Effect 3. Weight to it because of the gravity of the missions, and mini missions in-between to help simulate something more important going on. It was always worth the ten-twenty minute wait to see if your last teammate can withstand the onslaught by themselves, overcoming the obstacles and winning the day for the players. This is why it was so much more than just a horde mode, which is not even true because horde mode implies and endless supply of enemies you need to contend with anyway.
Regarding Dragon Age: Inqusition, there is a lot they can do if they use multiplayer. Flashpoints are probably the best model in a modern day context in how it could be done, but you need multiplayer scenarios you can interact with, plus your own "inquisitor agent" to act as your avatar for these mission. That can get old quickly if there aren't enough of them, or if there aren't enough pathways you can go on.
A similar mission mode like in Mass Effect might be a tough sell, because wave combat might be difficult to achieve. One possibility however is mass battles. Break down the multiplayer into teams of four, and the party must complete an objective for a single map. Multiply those teams into say 6 teams of four, each completing a separate objective, with a final battle to say take over the territory, with such objectives used to make the final fight easier.
So say one map is taking over a castle. You can have one team sabotage the castles defenses, one team eliminate the archer towers, one team try to break down the gates, and so forth, with a final battle in the courtyard being effected by how those objectives are fulfilled.
There is a lot of ways to make this unique, it depends on how BioWare implements it.