The household aggregate perspective
The shared fantasy is the 'reality' that permeates the living space in the hoarder's house. Inside it people live in a 'parallel' existence. They become inducted like in a cult or in a spy agency. People are forced to keep secrets to acquiesce to the pace, and dynamic, the place allows. And it becomes a den of indulgence, inactivity, and sickness.
The hoard isn't just a physical place; it's a 'magical' place in the anthropological sense of the word. The rules are different. Even the states of consciousness of people inside it change. In fact, even the nervous system and the immune system changes inside it.
Fig.1 - Entrainment - psychological states of the several family members tending towards the hoarder's
Having read about how the microbiome interacts with our nervous system and neurotransmitter production I'm quite comfortable affirming that the hoard changes its members on a biological level.
The changes a person undergoes can't just be dismissed as psychological, aesthetical, logistical-mechanical; they're biological as well. Inside the hoard we are its vessels.
It should truly scare anyone beyond the ugly sensorial spectacle. The hoard is 'demonic', if anything can be deemed as such. The hoard is a mental prison and it will influence its members under its dynamic.
People's lives will become oriented to protect the 'hive' - the cocoon. Living with this as a priority reforms the family system and the psychological organization of each member. The members can no longer serve their own cause, but must sacrifice for the hoard's logic.
It is a system. It is inflexible. And it's bigger than the individuals.
Each pile is a sacrificial altar; each object, an offering.
The ritualistic nature imposes a philosophical order - a worldview - and pressures its members to induct themselves with the same spirit.
The fact these patterns are maintained, and commemorated through recurrent sacrificial offerings, keeps the system going, and makes its subjects shaped to fit the hoard system - becoming sacrificial offerings themselves.
Fig.2 - An island of chaotic stability
Naturally, this closes the family system tighter; creates a cult mindset; and forces members to either stay or leave altogether, accruing an image cost of having shameful family ties. Conscious or not, it functions as blackmail.
Under the hoard system lies emotional regulation needs. The hoard forces actions to stop, people to slow down, and neither people nor objects can come and go as uncontrollably. The hoard is a system of control to force stability (although chaotic) into that place.