That said, you will have to re-implement machinery that rails gave you for free. If you're building a simple API, there will be obvious simplicity benefits. If you're trying to build a server-side rendered web application, you may long for some things that rails provided (of course, you can use libraries and create simpler patterns than rails provided).
Note that going the sinatra+libs (or any "micro" framework for that matter) route places a higher burden on the development team when it comes to documentation. If you implement a scheme for server side templating/rendering outside of what is provided, you will be in a world of pain in a relatively short time if you do not maintain good documentation.