Nest draws inspiration from Angular which in turn drew inspiration from enterprise application frameworks like .NET and Java Spring Boot. In these frameworks, the biggest concerns are ideas called Separation of Concern (SoC) and the Single Responsibility Principle (SRP), which means that each class deal with a specific function, and for the most part it can do it without really knowing much about other parts of the application (which leads to loosely coupled design patterns).
You could, if you wanted, put all of your business logic in a controller and call it a day. After all, that would be the easy thing to do, right? But what about testing? You'll need to send in a full request object for each functionality you want to test. You could then make a request factory that makes theses requests for you so it's easier to test, but now you're also looking at needing to test the factory to make sure it is producing correctly (so now you're testing your test code). If you broke apart the controller and the service, the controller could be tested that it just returns whatever the service returns and that's that. Then he service can have a specific input (like from the @Body() decorator in NestJS) and have a much easier input to work with an test.
By splitting the code up, the developer gains flexibility in maintenance, testing, and some autonomy if you are on a team and have interfaces set up so you know what kind of architecture you'll be getting from an injected service without needing to know how the service works in the first place. However, if you still aren't convinced you can also read up on Module Programming, Coupling, and Inversion of Control
