[fian]

So, if the Supreme Court rules that APIs are copyrightable, then wouldn't that mean that someone could use AWS with some, for example, Java code generation tools that created classes with method names comprised of randomly selected words from a dictionary - effectively performing a "million monkeys with a million typewriters" attack on the entire possible API naming space?

Publish the generated code on Github. Early on, you would need to test the generated code against publicly published APIs to ensure you didn't publish code infringing on existing APIs, however, over time you could "own" the remaining API naming space.

[dragonwriter]

No, while you might get a copyright that way, copyrights aren't patents. They only protect against actual copying and derivation. Independently authored works which happen to be similar, even identical, to some subset of a corpus are not a copyright violation. You don't get ownership of the naming space, just exclusive right to copy from your own work.