You observe, correctly, that just because a formal system S "asserts" its own consistency — by means of a proof which, in a meta-language M, is isomorphic to a proof of consistency of S — does not mean that you should therefore trust S to be consistent. Any inconsistent system which is rich enough to admit Gödel numbering (or an equivalent technique), and which has an explosive implication (so that everything follows from a falsehood), is able to prove its own consistency; although it would be interesting to know whether or not it allows you to derive "consistency claims" without passing through blatant contradictions of the form A & ¬A to do so.
The big deal with Gödel's Second Incompleteness theorem is that the only formal systems which can "prove" their own consistency via encoding in Peano Arithmetic (or an equivalent system) — and which is also able to prove that addition and multiplication are total functions — are in fact inconsistent. Even if we knew from first principles that we could not rely on internally proven consistency claims, there is the ironic twist that in fact such "proofs of consistency" are in fact proofs for precisely the opposite.
What this really means is that consistency is a bit of a chimeral property of a formal system to have. We are denied even the conceit of self-verifiability in totalizing formal systems. You can of course prove that a formal system S is consistent in another formal system M — but then why should you accept that M is consistent? Proving it so in another system M' is just pushing the problem away a further step. The consequence is that consistency of a formal system is a fundamentally negative property: a failure to be able to exhibit a contradiction, in which case you can never be sure if it is really consistent, or if you just haven't realized how to produce a contradiction in the system.
In the end, Gödel's Second Incompleteness theorem says that unless (like Gödel himself) you believe that humans somehow have a sort of occult-ish access to timeless Platonic truth, mathematics is subject to the same epistemological limitations as the natural sciences, in which formal systems play the role of theories and the discovery of inconsistencies play the role of falsification.