Uhhhhhmmmm… I’m that person you’re wondering about. I’m the absolute worst. At any given point, I might have 6-10 open bag spaces. 16-18 if I try to clean things up. 
You ask what takes up the space and it’s all, well mostly, “junk”. 
BUT YOU ASKED!!! SO HERE IT IS!! 
Necessary Stuff – I’m a raider and I run a good bit of M+, so I keep always on hand the various flasks, potions, foods, runes, and whatnot needed to be ready for anything. Throw the M+ keystone in on top of this and these can take 7-8 bag spots, especially because I try to carry enough to cover unprepared people in my group. Included in this are all currencies which aren’t in the currency tab and there are an unfortunate number of those.
Backup Gear – I hall pass myself for this since it’s actually useful. I always save the next previous thing to every piece of breakable gear I’m wearing so if something happens to break in a dungeon where I can’t repair, I can toss on the next best thing and keep going! This started with the hunter class calls in BWL when I found it higher DPS to leave my weapon equipped and just swap it out if Nefarian broke it. (At that time, I also carried grey bows to trade to other hunters mid-fight if someone was too slow to un-equip.)
Sentimental raid armor – I’ve gotten a little better about this since there’s nothing you can do when you’ve raided literally every raid since the beginning of WoW. Void storage definitely helps, but (for just two examples) I can’t put my crowns from Opulence in there and one of the tiger claws from original ZG is unique, then I can’t bear to put my Striker’s Mark in there since it would strip off it’s original enchant… add in all the legendary quest rewards like the MoP cape, the WoD ring, the Heart of Azeroth, my Legion artifact weapons (most of my characters have more than one), etc, etc … it starts to add up over 19 years.
Townwear – Back in the day we called tmog “townwear”! It sat in your bags and I still haven’t shaken the habit of carrying it. Most of my characters have a formal outfit of some sort (which often takes 3-4 bag slots), for example, and my only-beast-master hunter always carries a selection of favorite melee weapons.
Teleport Items – The Boralus ring, the Dalaran ring, the mole machine to the BRD bar, the necklace to the Black Temple, the Flight Whistle, etc, etc, etc… there are a lot more than most people likely even remember and I have most of them! I can get anywhere fast!
Grey Items – Dreamlure Candles, Sinrunner Horseshoes, Pet Collars, Pet Rocks, Fetishes of Hareek, and countless other beloved grey items with great flavor text are all stashed away along with items which were important before being made into grey items like the Urn originally used to summon Nightbane. Those last are most coveted as they can’t be obtained without having had the original item which no longer drops in game.
The Library – Readable books, scrolls, and even a few copies of game mails from NPCs to my characters are also kept. Non-soulbound ones are stored on a bank alt, but most from quests are soulbound.
Miscellany – Then there are the quest items which were never removed. The Tear of Elune from Leigion and the Moist Towelette from vanilla are just two examples, but other favorite items also fall into this category, like my Stratholme water (Just 1 calorie!) and my Tillers flowers which bloom on my body every time I die. When the scourge event came back around, guess who still had scourgestones?? This girl!
Soooo… TL;DR… Some of us just can’t help ourselves. To be completely honest, I don’t know bigger bags would help. There’s always some neat thing that three expansions from now, you can link in guild chat and get people to say: “Omg… you still have that?”
