The Collaborative International Dictionary of English v.0.48:

Inexpedience \In`ex*pe"di*ence\, Inexpediency
\In`ex*pe"di*en*cy\, n.
   The quality or state of being inexpedient; lack of fitness;
   unsuitableness to the end or object; impropriety; as, the
   inexpedience of some measures.
   [1913 Webster]

         It is not the rigor but the inexpediency of laws and
         acts of authority which makes them tyrannical. --Paley.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inexpediency
    n 1: the quality of being unsuited to the end in view [syn:
         inexpedience, inexpediency] [ant: expedience,
         expediency]