I don't agree that it doesn't tell us anything ... an inconsistent theory can prove all statements, yes, but not all with proofs shorter than its shortest proof of a contradiction. That is, if Peano arithmetic has a trillion-line proof that 3.2 is an integer, then it can prove anything in about a trillion and two lines... but it can't prove everything as easily as say (1+1+1)(1+1)=(1+1+1+1+1+1). It might be something special when a theory can prove its own consistency elegantly, sort of the way a human can have non-zero credence that s/he is usually rational.