But there must be something to it, as there are languages which allow only this kind of approach to software design. Can something useful can really be done in this paradigm?

I will show you how the language developed in the late 80s called Haskell. We will explore its syntax as well as philosophy behind its creation. At the end of a lecture we will even develop a simple REST application written in Haskell, in order to once and for all make this comic https://xkcd.com/1312/ obsolete.

Why would you want to learn Haskell? Some say it will make you a better developer, triggering ability to look at software problems with different approach. Is it true? You have to see it on your own.