When should you really use the visitor pattern

Ok before marking this as a duplicate let me clarify myself. I'm reading about the visitor pattern and its applicable uses.

I've stumbled upon this post: When should I use the Visitor Design Pattern?

and the user who wrote the first answer says as follow :

Now we want to add a new operation to the hierarchy, namely we want each animal to make its sound. As far as the hierarchy is this simple, you can do it with straight polymorphism:
...
But proceeding in this way, each time you want to add an operation you must modify the interface to every single class of the hierarchy.

Now, I mostly see why it's needed from his perspective, it's basically a way to cut compilation time by making it so not every time you want to add a new polymorphic method to a class hierarchy, the whole hierarchy will get recompiled.

But he's also saying that it's fine adding a new polymorphic method to the hierarchy as long as it's a "simple" hierarchy. But my question is when do you set your line and decide on what is simple and what is not.
Also, what if an hierarchy is a complex one, but adding a new method just make total sense to be and instance method rather than having the operation in a complete different class ?

Searching a bit more I found this article explaining the visitor pattern and it's uses http://ift.tt/1iuUqTl

The author gave an example where writing an instance method makes the object coupled to something and moving the method to a different class (The visitor) breaks the decoupling. This made more sense to me, but I'm still not quite sure when this pattern should really be used, the first argument of "changing the hierarchy time every time you want to add a new polymorphic method..." seems to me like an excuse because if a method seems to fit in the hierarchy it should be there logically, Assuming the Animal example was a really complex hierarchy and I would have decided to add make sound method, adding an instance method would be a logical choice (in my mind).
But maybe I'm wrong so I'm here asking for more insight about this, maybe someone could enlighten me.