Hmm, I'm not sure if codebase with millions of lines is 'medium' or 'large' but from my experience const is great even there. Of course, modifying existing code to become const correct in interfaces where previously it was not can cascade to a point where a majority of the code needs a rewrite, so I can see situations where adding const to an old interface can cause lots of grief.

But from my experience const really helps in enforcing directed graph constraints on logic and data flow which is great - and forces code to be easier to reason about.