If we want to play with Destiny weapons we'll still have Destiny. But after 3 years, a full sequel should be a new game, with only a slight nod to Years 1-3 at best. This isn't a true MMO, this is not WoW, this is an FPS and the success of FPS sequels usually rides on the new mechanics added to that core each iteration.
Bringing forward the existing weapon archetypes would dilute or possibly negate any advancements made. Because of the need to (try to) balance the game, the new weapon types would be limited because they'd have to be competitive with a boring old Lord High Fixer or Grasp.
What I envision:
At the start of Beyond Destiny, you select whether you want to import your existing Destiny character or create a new one. That character spawns into the tower. You can go to your vault, see all your old stuff, but whether you realize it or not you're looking at it to say goodbye.
An alarm sounds and you're summoned to the Vanguard. Cutscene shows that the Cabal Empire received that Outbound Signal and they've just jumped into our solar system in force. As they approach Earth, you and the Vanguard ask the Speaker to call upon the Traveler to help repel them.
The Traveler bounces. Our big silver ball leaves us.
The Cabal attack starts, and our brief playable intro mission begins. The Cabal drop a suppression field over the whole City, so regardless of your status you can't Super or use advanced movement perks. While the City, and the Tower specifically, gets hammered, the player must get the Vanguard out of the Tower to preserve our leadership. (Are they NPCs that we escort? Were they knocked out in the initial attack, so we're dragging them on a gurney that Ghost conjures up?)
It's a pretty short mission, just a run from the Speaker's lab to Amanda's ship over on the other side of the Tower. Just enough time to learn the movement mechanics of the game, shoot a few weak Cabal, all the basic first mission stuff.
We get the Vanguard off on Holiday's ship, hop into our own, and the next cutscene begins. The Tower crumbles, knocking our ship out of the air before we can escape. In one instant, our stash of gear and our ships have been destroyed, and we're dead.
Ghost can then resurrect us with a clean slate for the new game. Our old subclass powers were tied to our link with the Traveler, and that has at least been drastically altered, if not cut, by the Traveler's departure for parts unknown. So it makes sense that we need to discover new subclasses and powers.
Our gear is smashed to pieces with the Tower, our old ship, and our bodies, so of course we'll need to find new weapons and the slate is clean to make them in new and exciting archetypes.
And the environments? The tight, old-gen-restricted spaces like the Tower are rubble, allowing new and expansive zones. Who's to say we are even resurrected on Earth? If the story is going somewhere else, our allies or even our enemies could have scooped up our lifeless corpse and transported us any distance or time before this latest resurrection.
If we want another nod to our time in Destiny, perhaps a rescue mission to the rubble of the Tower is in order to save the Gunsmith. He's an exo, and he could stay pinned and damaged, but not deceased, for who knows how long. If we're using ported-in Guardians, we can access a broken Vault console and find all that remains of our gear is some weapons parts and armor materials.
Speaking of the Vault, with it's destruction Beyond Destiny would be open for a whole new system of gear management. Perhaps one with better indexing.