If all the shells above you were self supporting you'd be right, you shouldn't feel any more pressure as you go down, if anything you should feel less force because gravity decreases.
However a shell of liquid is not self supporting, and at the size of a planet pretty much all material behaves like a liquid more or less. This means something needs to be pushing back for the layers of material to stay where they are. That is the pressure you feel, and you can easily show it will increase as you go down (with each layer supporting all the layers above it).
If anything the shell theorem makes this worse because it means the top layer can't pull back on any of the layers below it, it can only be pushed back through sheer pressure.
However a shell of liquid is not self supporting, and at the size of a planet pretty much all material behaves like a liquid more or less. This means something needs to be pushing back for the layers of material to stay where they are. That is the pressure you feel, and you can easily show it will increase as you go down (with each layer supporting all the layers above it).
If anything the shell theorem makes this worse because it means the top layer can't pull back on any of the layers below it, it can only be pushed back through sheer pressure.