Hi Alexander, thanks for your post and update.
Well, this is all pretty interesting. We have an very good new theme, Boost, with some very nice features, the Drawer, but we are finding that the Drawer needs a lot more work to make it a "powerhouse" feature of moodle. It needs (almost demanding) that there needs to be much more user (either Manager, Teacher, or Student) customization.
For me, it is pretty good, except for two things: 1) All of the courses showing for Manager/Teacher, (which has just been fixed in the latest moodle), and 2) To remove topics navigation (which I can fix myself applying Gareth's suggestions.)
I am looking at the future of the Drawer. Looking ahead, yes, it could really benefit by allowing users to decide (i.e., pick) which features they want on the Drawer, and the ability for everyone to pick which specific courses show on it. Then the My Courses will really be from the perspective of "My.." and not Moodle's. I can see this happening since there has been overwhelming discussion about it here on moodle.org. I see the current Drawer as version 1.01. Yep, we need to have this "boosted" this to version 3.x.
Below is a screen shot of how my Moodle currently looks with the Drawer displayed. For me, not bad. The last two courses are actually "hidden" on my moodle, so I would like their color to change to my hidden color (see the main topic hidden color), or I would rather be able to say, "Just show my top 10 active courses and no hidden courses" because I should be able to get to the hidden courses by going to my Home. The student's view, I think correctly, does not show hidden courses. I also think that the ability to sort the course list would be desired by many. Also notice that no topics show in my Drawer, and that topics easily show in the main body (with Gareth's Collapsed Topics.) I think that you can see why I believe that showing course topics in the Drawer are unnecessarily redundant.