Why do the constructor of the derived classes want to initialize the virtual base class in C++?

The constructor of virtual base is constructed. It is constructed conditionally. That is, the constructor of the most derived class calls the constructor of the virtual base. If - this is the condition - the derived class with virtual base is not the concrete class of the constructed object, then it will not construct the virtual base because it has already been constructed by the concrete class. But otherwise it will construct the virtual base.

So, you must correctly initialise the virtual base class in constructors of all derived classes. You simply must know that specific initialisation doesn't necessarily happen in case the concrete class is not the one which you are writing. The compiler doesn't and cannot know whether you will ever create direct instances of those intermediate classes, so it cannot simply ignore their broken constructors.

If you made those intermediate classes abstract, then the compiler would know that they are never the most concrete type and thus their constructor would not be required to initialise the virtual base.

For some reason, the constructors B::B() and C::C() are trying to initialize A (which, again in my understanding, should have already been initialized by D at this point):

But what should compiler do if somebody constructs C solo? The final object D will call the constructor of A but you define constructor to C which implies that it can be constructed but the constructor is faulty cause it cannot construct A.