All analysis is based on the following high-level assumptions:
Core loop = quest -> explore -> combat -> improve (stats)
Short-term engagement = consistent, measurable power rewards
Mid-term engagement = difficulty modes that push the player back into the short-term cycle
Long-term engagement = create multiple characters
Primary player behavior motivator: Achievement through power
Procedural item generation & manufacturers: Like Diablo 3, Borderlands 2's primary reward loop is driven through the itemization. Which again makes procedural item generation key for the same reasons. The manufacturers concept to bucket the feel and playstyle of weapons makes the system still feel custom and rooted in the narrative. In addition, the wide variety of weapon mechanics, even the hokey ones, are necessary to make sure the loot matters.
Elemental Damage Types: When combining power with a skill-based game, the biggest challenge is to minimize the 'bullet sponge' feeling when fighting humanoid enemies while still providing a challenge. Elemental damage types and enemy resists reframe the 'bullet sponge' to instead be communication to the player that they are not using the best possible strategy.
Whenever you are shooting an enemy forever in Borderlands you know you should try a different weapon. This of course also drives the player back into the itemization loop to get the right weapons to face the challenge at hand.
Class skill trees: The secondary reward loop of leveling up to unlock skills is very successful in Borderlands, because shooter game players generally have playstyle preferences/needs, which are supported in not just the base classes, but in the how they specialize over time. These also make it interesting to try new ways to play the same class and try out other classes. Each also assists in co-op play to create roles that allow for synergistic teams.
Overall, Borderlands 2 was a really tight game. The team did a great job editing and only including systems they needed to support the game loop.
Vehicles: Although useful for co-op play, vehicles overall were more of a pain and interruption to the flow of the game when required for specific missions.
Weapon Attachment/Mods Crafting: Borderlands embraces randomization completely, but this is somewhat dangerous for engagement in a shooter, where skill and pre-determined playstyle preferences are big factors to feeling successful and smart. Adding an aspect of itemization agency for the player through crafting weapon customizations could help give players an avenue to get exactly what they want and reduce grind fatigue when the RNG gods aren't on your side. I'd allow for crafting of scopes, silencers, mag extenders, etc. I'd also consider adding mod slots to weapons or the character that compliment their chosen playstyle. Mods would give passive effects, like fully reload a sniper rifle after N consecutive headshots. Or a damage modifier when attacking from above an enemy. This would give even more items to collect and methods to further specialize your playstyle. They could also help double down on a role for co-op.
Vehicles: I'd either remove the driving of them and make them AI controlled making the player a gunner or spend more time tuning to make them super fun. If time is spent on them, they could become a more interesting component in the game by giving them progression and item slots of their own.
Hats!: I'd add far more customization options and unlocks for the character's looks. Overwatch style skins that unlock through progression, achievements, and Badass Rank would give another motivator to engage in those systems, especially when the player has collected their near ideal playstyle loadout.