I apologize if this question has been asked before. I've searched SO somewhat and wasn't able to find it.

I'm just curious what the rationale behind this design was/is. Obviously I understand that private/internal members of a base type cannot, nor should they, be exposed through a derived public type. But it seems to my naive thinking that the "hidden" parts could easily remain hidden while some base functionality is still shared and a new interface is exposed publicly.

I'm thinking of something along these lines:

Assembly X

internal class InternalClass
{
    protected virtual void DoSomethingProtected()
    {
        // Let's say this method provides some useful functionality.
        // Its visibility is quite limited (only to derived types in
        // the same assembly), but at least it's there.
    }
}

public class PublicClass : InternalClass
{
    public void DoSomethingPublic()
    {
        // Now let's say this method is useful enough that this type
        // should be public. What's keeping us from leveraging the
        // base functionality laid out in InternalClass's implementation,
        // without exposing anything that shouldn't be exposed?
    }
}

Assembly Y

public class OtherPublicClass : PublicClass
{
    // It seems (again, to my naive mind) that this could work. This class
    // simply wouldn't be able to "see" any of the methods of InternalClass
    // from AssemblyX directly. But it could still access the public and
    // protected members of PublicClass that weren't inherited from
    // InternalClass. Does this make sense? What am I missing?
}