QCoreApplication::Type vs. QApplication::type()

Wouldn't it make sense to make the QCoreApplication::Type enumeration reflect the available application types in Qt 5, and propagate the getter from QApplication::type() to QCoreApplication::type()?

enum Type {
    Tty,
    GuiClient,
    GuiServer // # deprecated
};

It could offer values like Tty(or even simply Core?),Gui,Widgets instead.

It is very confusing that currently QApplication::type() returns Tty when QGuiApplication was instantiated. As a side effect, instantiating QWidget in a GUI application throws a misleading fatal error:

#include <QtWidgets>
int main( int argc, char* argv[])
{
    QGuiApplication a(argc,argv);
    QWidget w; // QWidget: Cannot create a QWidget when no GUI is being used
    w.show();
    return a.exec();
}