The problem with benchmarks is that they don't really correspond to reality. Your app is not a simple test app. Your site will not be running on my MacBook Air. Your users won't have the usage patterns my script does.
"We are building an API. Rails has extra components which aren't used but might cause overhead. Here is how to remove it."
I think that's a valid enough use-case.
The README itself says Rails::API is faster, so not sure why a simple benchmark to back that up isn't a good idea.
edit: It really boils down to another way to visualize the overhead vs just listing what's been removed.