You can just build your tree data structure and develop operators to work with them in Lisp. There's nothing that restricts you to using lists. So what's the point of "replacing" them (even if such a thing were possible without "replacing" Lisp)?
Cons cells give you binary trees. It is possible to encode any arbitrary tree as a binary tree. However, this does not mean that the expression of algorithms over such left child right sibling encoded trees is identical to one over trees with some higher branching factor. So the cons/binary situation will at the least require some additional layers of abstraction to simulate various traversal patterns of the n way tree on the encoding binary tree.
There also physical/efficiency concerns. There's a reason databases use highly branching trees.