Not all data is complex enough to merit a map: modeling e.g. a list using lists is perverse in that you're using degenerate single-item maps to model what is a simpler data structure.
And what does a lisp based on maps look like, if this language preserves the homoiconic nature of lisp?
The argument by analogy that a lisp "should" have a "better" data structure than a cons cell because lisp lambdas support multiple arguments, unlike pure lambda calculus, doesn't hold water. Lisps--and even Scheme, which is often incorrectly taken to have as a design goal to be minimalistic to the point of consisting of axiomatic primitives--do not deal in pedantic adherence to theory. Limiting lambdas to a single argument is pointless whereas a cell happens to be minimal yet extremely useful in practice.
Other have written lisps atop vectors as the primitive data type. That's an idea that makes more sense: it's a generalization of the pair to arbitrary length.