We already are in the state you describe, except for patents. The doubly linked list is patented [0]. Selling something over the internet was patented [1]. The list could go on and on.
Every major software company has so many patents that they could find an infringement in almost any software company.
Why hasn't this happened? Because, like copyright, someone needs to actually bring suit. That doesn't happen that often. It happens more often with patents in the form of patent trolls actually, and there's no reason to believe api copyright suits would happen more often than patent suits... I think api copyright suits are actually going to be less lucrative and harder to prove on average.
So yeah, it seems like the current state of software patents is already far worse than APIs being copyrightable would be, and yet the sky is not falling, civilization is not collapsing, and business continues like usual.
