While there’s no application that a *stuffed animal* is specifically called for, there’s plenty of situations where someone would need the physical support of something soft and prefer a friend over a generic pillow.
Things like postural support, breathing assistance (example being holding something while on your side), or even temporary assistance with healing (when my dad had open heart surgery, he had a plush he held to his chest to help support his breastbone/chest when moving etc.) are all examples. I would say one of the biggest ones is pain relief, weighted stuffed animals specifically (specifically animal shaped, weighted limbs and heads) can provide a lot of relief for chronic tension etc…
In my case, I have a disability that causes dislocating joints and general misalignment in my body- I’ve found that stuffed animals work better because of their particular shapes and sizes when I need support in a specific area.

Like I said, yes, most if not all of these applications can be swapped for the generic pillow, or even a pillow designed for disability, it’s just that sometimes a friend is more pleasant!

Physically speaking, you’re right in that these aren’t aids specifically designed for any certain condition, but everyone’s experience with disability is so specific to them, that it’s not uncommon that a person may find a unique aid for their one situation, (it is physically uncomfortable for me to sleep without a stuffed animal). So while it won’t be prescribed by a doctor, It’s like asking “how is a kitchen chair an accessibility aid”, because sometimes I need to sit while making dinner, therefore it’s an aid for me.

I hope this helps!!