I will probably improve this article in the future, but the summary is that I surfed around and tried to find a software package that allows me to create 3D models for games and I came to a conclusion that all of them assume a lot of mouse clicks. The amount of mouse clicks and movements is so huge that I came to an opinion that the only decent way to "draw" those models is by writing functions, having the computer to draw a lot of components for the user.
If 3D models are written in a form of a programming language, then a side-effect of that kind of 3D modelling is that the model will inherently have structure, info about joints, possible movement constraints, etc.
I do not know, how it will actually work out, but currently I imagine that on one screen or area of the screen there would be a 3D image of the model and at the other area there would be the IDE, which can be a classical IDE with a programming/modelling language support add-on. There would be a periodic model "recompilation" attempt and the image would represent the last successfully compiled version of the model.
Technically all of that is doable in a modern web browser, provided that the 3D model does not contain "too much" data-points.
Out of topic, but relevant: I'm truly happy that AT LAST I found a decent screen-casting software for Linux, Ubuntu Linux: http://www.screencast-o-matic.com/. It's main peculiarity is that IT WORKS and produces a video with a proper quality. It's not flawless and it does jam/crash from time to time, but as of September 2013 it is the best that I have found.
Check out VokoScreen instead.