> Self referential consistency makes sure I do not make errors within the logical model I have set for myself. It does not help me build better models but once those models are built it helps me to compose programs that do not break the invariants in the chosen formalism.

I think this is a valid point.

But I am less convinced about the second part. I feel that better type systems do help one model the world better (while retaining the consistency checking that you mentioned). In my mind at least having more/better "type tools" is like having differently shaped pieces in your lego tool box. You can create better models for yourself, because the pieces allow you to. And the more experience you have with them, your modeling abilities also improve.