Yeah was about to say, this seems like a supplier-side issue.
Just like how we humans insist on putting needless things into boxes, although it can be helpful to protect the all-important box during transport of course so it won't collapse!
I got my dog one because she loved being covered by blankets, and she did the same thing. And then insisted on having a blanket over her anyway. On the plus side, she loved the bed in her own way.
There's a company that makes things like this that have a hard shell covered with felt (I think felt?); cats can be both inside, or on top. I'll have to see if I can ever find it again; it looked like the cats were quite pleased with that kind of design.