In other words, what parts of Destiny (other than the obvious large-scale stuff) do you want to be maintained across the rest of the franchise going forward?

For me, it's the great sense of physical location the game gives, and using in-universe proxies for real life technical game stuff. For example, the way you always see yourself travel from location to location. There's never any skipped time, you watch your ship fly from the moon, out to space, to Mars, and then down to the multiplayer map you're playing on. It helps to keep things so grounded. But on top of that, they use these as substitutes for loading screens, connecting networks, etc. So instead of "loading a map", I'm "traveling to the surface". Instead of "joining a friend's party" I'm "on my way to their location". That sort of stuff is just great for the overall experience.

I'd even go so far as to suggest that Bungie should use it for more things. Instead of "being dropped from the game world", make it something like "your ship needs urgent maintenance" or something along those lines. Whatever can be done to keep us in the universe, even when things are going wrong, would lend so much to the universe.