I honestly think that, like with a lot of collecting, it's mostly driven by autistic and mentally ill people fixating on specific items because those items bring them comfort and joy in some way. It's really easy to fall into that trap with things like plushies because they're soft and comfortable and huggable - they make you feel good, and they're easy to have around since they can just go on the couch, or on your bed, or whatever. I've seen some claim that certain plushies have a specific consistency and softness that makes them especially good for trauma victims, particularly children with trauma, and can help them calm down during anxiety attacks or PTSD flashbacks. So it makes sense that the biggest collectors of these plushies would be groups that are probably suffering from trauma and anxiety, who are prone to hyperfixations, etc.
It's not really that different from the guy who collects a hundred different Transformers toys that are nearly identical except for the name on the box and the paint job because when he was a kid, watching Transformers cartoons or playing with Transformers toys brought him joy and comfort and he isn't ready or able to let go of that source of joy and comfort due to autism, trauma, mental illness, or whatever. How many little girls had loads of stuffed animals in their bedrooms as kids that they might have retreated to when they were stressed or scared or hurt? That's where it comes from, I think, right there.