Is it worth making independent controllers in angular directives?

Question

Angular

Let's say a directive controller that calls a service that makes requests to get something. And in general, in general, controllers that do not overlap with the main one from the module.

Answer 1

Let's say the controller has directives that make requests to get an array

And what about the controller? Usually services are engaged in it. In general, the controller of the directive should only deal with what is needed within the framework of this directive (that is, it contains the logic of this directive, let's say the link is needed to bind the logic and the DOM). If you need to take data there, then take it.
As much as needs. It is important that the directives are isolated pieces of functionality that have no idea about the implementation of the outside world.