That problem has little to do with java. OpenGL is not designed for UI's. There is no native support for font rendering and the way modern graphics processing works (VBO's, Shaders, etc) is in stark contrast to how GUI frameworks are traditionally build.
By the way, AWT/Swing may actually be using OpenGL in the background "under the hood" so to say. The implementation details are not strictly enforced and alternative solutions are possible. On Windows for example you can choose between either a Direct3D or OpenGL implementation. Maybe even other alternatives. So the problem is not so much in OpenGL + Java.
The real problem is finding a proper GUI framework that works well with OpenGL and is also easily integrated (or even written in) java. In my spare time I tried to developed such a framework as a hobby. It really is not easy to make good use of modern rendering techniques when building a fully functional GUI framework.
Maybe have a look at this thread: http://forum.lwjgl.org/index.php?topic=6883.msg36272
On a side note: I once worked on a project which used Qt with java and OpenGL rendering. Its not "nice" but its definitely possible.