I’m of the mindset that there is definitely room for both kinds of loot hunt within a game.
The World Drops are great for those, “Oh! A piece of candy,” moments. You’re not exactly looking for something but when it does drop, it’s a nice surprise, even when it’s another ASMD 
When it comes to dedicated looting, I think one needs to set into place a Spectrum of looting. This spectrum exists to allow for all players to get what they want out of a grind.
I’m going to draw a lot of parallels to games like Destiny and a GDQ discussion on Diablo 3’s Loot 2.0 when it was first implemented.
The TL;DR version is that Generosity leads to further engagement rather than diminishes it. What does that mean? Read on.
(Please understand this is only my opinion and not meant to directly prescribe or direct other players experience. This is anecdotal and meant to provoke discussion and perhaps evoke positive change for the game we all love to play)
Borderlands, much like other looter shooters has many levels of RNG. At the lowest level is the item, then the items parts ( +- stats ) and of course, anointed bonuses.
At the lowest level, players should be able to get the item with a decent amount of frequency. Destiny does this now with weapon frame bounties and the Chalice of Opulence, as examples.
This enables player to “get the gun.” It’s not a perfect gun or “god roll,” but if you want the gun for your collection, there it is. This level is meant for players who may only have a limited amount of time to play or isn’t interested in further pursuance of the God Roll.
In Borderland’s Targeted Loot Pools, this is answered by allowing players to farm Graveward for the Ward shield mod, as an example. Ideally, this mod would drop with a decent amount of regularity do that plays can collect it, try it, and see if they want to pursue the perfected version.
In the next step, or steps, is getting the PERFECT roll of an item. In Borderland’s case, this means getting the right mods, parts and anoints.
If the first level of generosity is answered with regular drops of an item, then a player has more chances to get that God Roll.
Drawing a parallel back to a Destiny, once players finish a Weapon Frame bounty they are guaranteed the gun. Not a perfect gun, but they get the done. If they keep getting the bounty, they can keep getting guns until they get that God Roll.
Diablo’s Loot 2.0 allows for greater generosity so that I’m even if you do get multiples of a single item, YOU can compare which one is the roll you want.
This innate generosity changes the mindset of the player. It goes from, “I just want the gun!” to, “I wanna keep farming to get the perfect gun!” Players love seeing those gold drops and get those hits of dopamine in the brain. There’s anticipation and excitement for each drop.
People want to see drops and seeing those drops eggs on for more farming. Generosity also allows for players who just want the gun to look at other sources and play more of the game, rather than get burned out on one source and putting the game away due to frustration.
This generosity also takes a more casual farmer into a more hardcore farmer and this leads to greater retention thus, better numbers for the game.
Overall, I believe that loot generosity has good merit. I’m not advocating for “free loot,” or some variant wherein. There needs to be something there to protect the player from running the line of least resistance. However, this path should not be obtuse nor should it lead to low reward numbers.
I think adding dedicated loot pursuits is a good first steps, but I think further refinements could be implemented to enable higher quality of experience for all, regardless of time put into the game.
As you can see this is something I’ve thought about for a while. 