"weird dialect of C++98" - WTF? What is this dialect you speak of? Do you need to pass --weird to G++ to get it to compile? Of course not! It's using the same C++ every other C++ app in the world is using. Both C++98 and C++11 are supported. It doesn't REQUIRE you to use C++11, but that is a benefit not a drawback.
"it has its own object model" - Of course it does, that's because C++ does not have one of its own. QObject is there to provide for the introspection that C++ lacks. Once you have that introspection you can start communicating with other objects. I fail to understand why this is a disadvantage in your eyes.
"networking stack" - Of course. Why should it not? It is an cross-platform application framework.
"container library" - When Qt began the STL was fragmented, not standardized, and poorly supported. Yet containers are useful. Qt kept them around because they turned out to be better than the STL containers. They're a balance between raw performance and the "bloat" of pure templatized containers. Externally they end up being 100% compatible with the STL.
"threading library" - It was only extremely recent that C++ got its own threading, and it's just very low level threading. Qt threading provides a nice usable wrapper around threads (which are native C++ threads underneath if built with C++11), and the ability to easily communicate between threads with signals/slots.
"graphics primitive library" - Why not? Seriously, why not? Isnt't that the whole point of a GUI toolkit? Underneath it draws widgets using the native controls, if available, or uses its own if not. That's why the widgets look like native controls on Windows and Mac, because they ARE native controls! On X11 it will draw its own. It doesn't use Cairo, why should it use Cairo, who made Cairo king that we all have to bow down before it?