It is an open question whether what I have called Hilbert's ultrafinitist program is possible, that is whether a natural base theory can prove the consistency of natural stronger theories. Please see
Is an ultrafinitist Hilbert's program doomed?
So in this sense the Second Incompleteness Theorem is not redundant: there could be natural theories which prove natural stronger theories consistent.
In any case I'm of the opinion that proving self-consistency is a good test for a theory; that is, if a theory can't even prove its own consistency, that is a good reason not to accept the theory.
