The horders I dealt with during my tour of duty had already passed to the next world, but you still had to protect yourself mentally each morning lest you go crazy/question existence/get depressed/etc (happened to a couple of people I worked with, although I don't rule out the possibility that crazy is attracted to this kind of work). For each item in every bedside table, every piece of furniture, every picture, every computer, you had to put aside the memories the deceased person may have had, the reason the deceased held onto the item until the end, the data contained within and make a split-second decision: box or barrel.
Barrels were massive rusted oil drums that we used for collecting garbage. Boxes were used to transport the salable "smalls" for auction. If you were caught considering the saleability of an item for too long you'd soon hear your boss's voice from across the room, "barrel it!"
One time I came across a pair of filing cabinets filled to the brim with research and lecture notes on Egypt and the hieroglyphics. I had already pieced together parts of this person's life to form an image of them - old-money spinster who traveled the world lecturing and having adventures, including sneaking in to China from Hong Kong in 1976 - and their life work was contained in these filing cabinets.
"We can probably get fifty bucks a piece for the filing cabinets; barrel the rest"
For a team of three, two hours per room was budgeted, so everything that was dear to a person over the course of their 70-year life would usually be processed within two days.
Regarding hoarders, the main differences between a dead hoarder and a living one are 1) the fact that you don't have to deal with the emotion as per the OP, and 2) there is no superficial "cleanup" the day before the cleaners arrive. The house is exactly as the hoarder left it as no-one thinks the day before they die, "If I were to die tomorrow I'd be aghast if they found this!"
I know this sounds ridiculous but I would expect a living hoarder would at least manage to dispose of the bucket of feces and used tampons next to the couch if they knew some cleaners were coming. Even hoarders have pride, y'know.
The house with the bucket of tampons was the stuff of legend. Even today, 15 years later, if I were to contact my former boss for a beer it wouldn't be long before the story of that place came up. Along with the tampon-and-poo bucket, the final defacation of the former resident in the sweat-crusted outline on the green velvet couch where the they had spent their final moments is still a vivid memory. The stench, using shovels to scrape up the person's life from where it was stuck to the carpet and fill barrel after barrel, my boss's sense of humour ("whaddaya suppose she used this for?!"), how quiet everyone was on the ride back to the office, showering for an hour afterwards.
Understandably, after working this job for a while I went through an extremely minimalist phase. Even now I pause before most non-consumable purchases. I keep nothing that I wouldn't want someone finding when I die.
I think while many hoarders fear the memories of the past being forgotten, HNers tend to fear being forgotten themselves.
Of course as per the OP, there were good parts to this job too! The pay, for starters, was decent. And discovering some bondage equipment or some naked polaroids of the former resident and their girlfriend was always good for a chuckle and a reminder to stop taking yourself so seriously and enjoy life a bit more.