Not having a campaign won’t fix the problem. The problem is that Bungie has focused so much on mythology and world building, and very little in story. They just need good stories to tell. It’s really that simple.

God of War does a fantastic job of doing both.

Sometimes, you’re not really told right away what’s going on in an area, or what it’s history is, nor do you know the names of the people that you encounter. But you piece this together as you go along, learning things naturally.

A good example of this is what’s happening in Alfheim. The place is a mystery as soon as you arrive. You only know what your goal is and where you’re headed. But there’s a lot going on there, and you slowly put the pieces together as you go along. But you don’t learn everything, and by the time you’ve accomplished your goal and leave, you’ve significantly changed the outcome of the realm’s events.

When you’re given exposition, it’s to contextualize what you’re doing, and it’s usually built off of information that you’ve picked up on at least a bit beforehand.
A great example is the backstory that you’re given about a certain giant. You are told who he is, and a portion of his backstory that will be relevant to you, so when you find him, you understand what has happened, who is responsible, and how this all plays into what you’re doing there. None of the relevant information could be learned through gameplay, so in this instance, the exposition was necessary, otherwise you’d just be in a curious place without any emotional weight.

The issue with Destiny is that Bungie uses exposition as their only storytelling tool. The places that you visit never tell a story on their own. Their history is told to you through radio by the characters, but ultimately, it has no impact, because it’s not relevant to your actions, and most of the time, the location of the exposition doesn’t matter.

When you walk into a room in Destiny 2, you never get a “what happened here” moment. Most regions are as lifeless as the last. A building could hold countless stories within the walls, but the only story that you get is told to you over comma while you’re distracted with shooting enemies that are just standing around, or who spawn in. What were they after? What exactly are they doing in this building? Is there something about this particular area that is relevant to them or us?
Nope. If there’s any history or purpose that can’t be fed to us during the mission, it will likely be told to us through a single scannable item. The only interesting rooms tend to be the last room of a mission, because that’s what has been given the most context and interaction.
And unlike Alfheim, our actions pretty much never have a permanent impact on a region, much less one that can come back down the road.

What consequences are there for activating the Array in D1?
What impact did destroying the Heart in the Black garden have on the Vex?
What has the vanguard done with the hole in the subway wall that leads directly to the black garden?
What became of the Warmind room where Aksis was?
Has SIVA been defeated in the Plaguelands yet?
Do we just not work with Petra anymore?
What’s become of the Hellmouth?
Are we still trying to take out the Skyburners’ command one by one?
What all’s being done with the Dreadnought?
And the Cabal bombs aboard?
What’s changed for us Guardians since the traveler awoke?
Since we’ve defeated Ghaul and got our light back... why are we still on Titan?
Why is the red legion on Nessus?

All these questions introduced through Destiny’s monster-of-the-week storytelling are never answered, and most were never contextualized either, so you feel nothing going into them, and since you don’t change anything because of the exposition that you are fed, nothing that you do sticks with you (and it usually has no lasting effect for others).

At least in this DLC, the adventures are more focused on the region itself, while also feeling a bit less menial that something like the “boosting the comms network in the EDZ” side quest, or the Prophecies on Mars.