I agree. Personally, I espouse the "copyright should not exist at all" viewpoint. However, I think in the current legal framework, APIs are clearly copyrightable. However, re-implementing the APIs should obviously be allowed under fair use.
Remember that copyright exists solely for the purposes of increasing the production of otherwise-easily-copyable works that take time to create but then are "worthless" (i.e. the marginal cost of each additional copy is ~0 or negligible).
From the Constitution itself:
"[the United States Congress shall have power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries."
I can see how one can argue that software itself - the actual code - will benefit in the same way (though the myriad successful open source projects and SaaS platforms seem to suggest it's not necessary......). However, I think it's pretty dang clear that limiting the copying of APIs will broadly lead to less software being created. It's well established that, for software, ideas are cheap, and that competitive advantages primarily come from excellent execution and excellent VC funding. If someone re-implements your API and your business folds, it's not because your API was your secret sauce and they stole it. It's because their re-implementation - which, by definition of an API, must be "the exact same thing" - was better than yours. They produced a better product, and the market rewarded them for that.
So, for a legal framework whose purpose, as outlined in the constitution, is to promote the arts and sciences, I think it's pretty clear what the path forward is.