An inner interface inside an outer interface is not supported in Apex?

As the documentation says in this entry Differences Between Apex Classes and Java Classes

 - Inner classes and interfaces can only be declared one level deep inside an outer class.

So you are allowed to declare an interface only inside a class (not inside an interface). I think you can still acquire the desired output of having a bunch of interfaces inside a "namespace". Just make it abstract, so it cannot be instantiated

public abstract class Access {

    public interface Context {}

    public Set<Id> accessibleContacts(Context context) { 
        throw new NotImplementedException('You must implement the accessibleContacts method');
    }

    public class NotImplementedException extends Exception {}
}

The main reason why this is not supported, is that Apex isn't Java. When salesforce.com sat down and started designing Apex, they created a BNF that they felt could be implemented in a reasonable amount of time, have enough language features to be useful to the majority of customers, and be generally secure and stable enough that it wouldn't crash frequently.

Even back then, though, developers had a very good chance of running into Internal Server Errors if they didn't strictly follow the code patterns laid out in the documentation. Things like deeply nested classes, nested interfaces, etc were simply out of scope for the project, as they would have been too complicated, and could be solved by other, simpler patterns. The compiler was too fragile to handle large new features, and many of these probably would have broken Apex completely.

Think of all the things we don't have from Java: events, nested interfaces, default parameters, lambdas, anonymous inner classes, deeply nested classes, nested interfaces, java.lang.Reflect, nested namespaces/packages, import statements, there's a huge list of things that are just different or missing. Apex was thrown together in a very short amount of time (as far as compilers go), and the fact that it worked as well as it did initially was a surprise to some.

I don't think you can get an official answer for why it's not supported other than a vague "we didn't have time" or "it was too complicated" type answer. Just know that the old compiler could not have handled this type of code, and today we're still in compatibility with that old compiler. For now, if you want interfaces grouped together, put them inside an abstract class, or group your classes into unlocked packages (or not, just use folders into your repo!).

If you're not yet using DX, you may want to start leaning in that direction. It offers the sort of organization you're looking for, just not on the server side. It's not likely we'll see many of these features any time soon, although I would be pleasantly surprised if they were.