The advantage of storing them elsewhere is not quite clear (unless you have hardware support for things like shadow stacks).
You'd have to argue that the cost of moving things to this other page and managing two pointers (where one is less powerful in the ISA) is meaningfully cheaper than the other equally effective mitigation of stack cookies/protectors which are already able to provide protection only where needed. There is no real security benefit to doing this over what we currently have with stack protectors since an arbitrary read/write will still lead to a CFI bypass.