In my experience this exponential expression blow-up is less the result of the approach of decomposing into a minimum of primitives, but rather a result from repetition in expression trees:
If we make the analogy from Bertrand Russel's Principia Mathematica, he derived fully expanded expressions, i.e. trees where the leaves only may refer to the same literals, everyone claimed this madness underscored how formal verification of natural mathematics was a fools errand, but nevertheless we see successful projects like metamath (us.metamath.org) where this exponential blow-up does not occur. It is easy to see why: instead of representing proofs as full trees, the proofs are represented as DAG's. The same optimization would be required for EML to prevent exponential blow-up.
Put differently: if we allow extra buttons besides {1, EML} for example to capture unary functions the authors mentally add an 'x' button so now the RPN calculator has {1, EML, x}; but wait if you want multivariate functions it becomes an RPN calculator with extra buttons {1, EML, x,y,z} for example.
But why stop there? in metamath proofs are compressed: if an expression or wff was proven before in the same proof, it first subproof is given a number, and any subsequent invocations of this N'th subproof refers to this number. Why only recall input parameters x,y,z but not recall earlier computed values/functions?
In fact every proof in metamath set.mm that uses this DAG compressibility, could be split into the main proof and the repeatedly used substatements could be automatically converted to explicitly separate lemma proofs, in which case metamath could dispose of the single-proof DAG compression (but it would force proofs to split up into lemma's + main proof.
None of the proven theorems in metamath's set.mm displays the feared exponential blowup.