why the hell so many packets has qt*
Well, Qt is one of the most popular, if not the most popular, cross-platform GUI framework. The whole K Desktop Environment, which BTW is also quite popular at least in Europe, is build upon it. KDE comes with many applications, like utilities and games. So all in all it's no wonder that Desktop Linux distributions provide a lot of packages that depend on our cute framework.
why everything with qt in its name takes ages to compile
Can't say much about specific applications, but building the Qt libraries themselves doesn't take ages. Just did it yesterday, on Linux, took under 14 minutes.
Is there a way to cross out qt* completely?
Don't remember, better ask the guys at Gentoo.