Because it has a lot more "ceremony and structure". Sinatra is a Rack app. It hides the raw boilerplate from you just like Rails hides a lot of the boilerplate you end up putting into a Sinatra app of any significant size.

There's a continuum of "more manual work" <----> "more framework", and there's no one right answer, even for something like a JSON API.

Rails is a Rack app too. While I agree there are diminishing returns the lower in the stack you go, your original reduction is misleading.

The choice between Sinatra and Rails can reasonably be debated, but there's little reason to write a JSON API in Rack unless you need control of protocol details that neither abstraction provides. Sinatra/Rails are frameworks, Rack is middleware.