Yep, this. I suspect that those who are getting the "it takes forever" feeling from it are often doing exactly this thing. I always look at the loot/store and do my equipping after every mission, and it seriously doesnt take long at all, so it never reaches the point of feeling like it takes too long and making me not want to do it. And you get faster at it as you learn the game more.
Well, to be fair, I don't think I'm too far out of the norm on that feeling. If the fix for a problem in the game is telling players to play a different way, then either the devs or the players are looking at it wrong. Now I'm open to the idea that I'm the point of failure here, but I kind of doubt it. I'm usually the type that is all about loot comparison. I'll whip out the spreadsheets and sit and autoattack the training dummy and then tweak things slightly and go at it again. I get plenty of enjoyment out of mindless kill > loot > kill bigger things > loot better things > repeat gameplay. I've got hundreds of hours across Torchlight 1/2, Titan Quest, Path of Exile, The Incredible Adventures of Van Helsing, and plenty of other Diablo-likes. (Although not the original Diablos for various pointless reasons) And also plenty of other rogue-like loot driven games, or just RPGs with some loot and optimization component, or MMOs, or whatever. I say all that not to convince people the I am a gigantic nerd, because some things go without saying, but just to point out that loot overload is usually a pool into whose deep end I willingly dive.
That said, I don't think there's a single point of failure here that is bothering me. I think it's just too many little things taken all together. We've got just piles and piles of loot, we've got interchangeable loot (in that many pieces can go in different slots), we've got an overabundance of slots (3 or 4 per 'limb', across up to 9 'limbs'), we've got 4 different 'characters' to outfit all of which use the same gear, and we've got non-specific loot (while each piece will roughly have one main stat, sub-stats can be pretty much anything as far as I can tell).
The standard fixes for these things are already there in the long history of loot games. If you're going to have multiple characters to oufit, they all have different gear. The rogue wears leather and uses daggers, the mage wears cloth and has a staff, etc. etc. Obviously the fantasy tropes don't apply, but I'm just talking about the game mechanics. Somewhat arbitrary limits at least mean that when you ransack the dungeon you now only have to compare items specific to each class when you upgrade them. Likewise, the problem of too much interchangeable loot is narrowed down in standard games by things that naturally fit one slot. Gloves go on the hands, boots go on the feet. BD's equivalent is gloves that can go on hands, feet, ankles, elbows, and hang off your nose. And might possibly have different effects depending on where you put it! Again, the limitations help to make choices more clear.
The non-specific loot can be sharpened so that you always tend to get the same stats on the same things, avoiding the problem of upgrading your weapon but tanking your shields, so you have to change the shield but now you've killed your propulsion stats, so you upgrade that but now your hacking has dropped, etc. etc. Too many stats creeping in to too many areas makes for constant fiddling to get things right.
As far as just plain too many slots, that could be rectified by, (surprise) just having fewer slots. For balance purposes, the average 3 slots per thing could be reduced to 1, and items could just have 3x as much stat allocation as they do right now.
Now I'm not advocating for all of this together, that would be overkill. And the solution doesn't have to come from the standard loot-driven game checklist. Arcen is smart people. If the standard solutions don't look good, come up with some new ones! But I think it at least deserves a hard look. I usually get a kick out of being able to quickly sift the good from the bad loot and then comparing the good stuff together and picking an overall winner. That gives me that little nebulous feeling that we call 'fun' in my frazzled brain. BD is not flicking that switch, though, in the loot department. It feels more like filing my taxes. Endlessly poring over boring details while knowing that if I get something wrong an enraged robot will come blow me up. At least I think that's how the IRS works.