The date added column contains date&time and therefore it is quite wide and most often it is only needed for sorting (e.g, most recently added appears at the top). Nevertheless, you can resize it the same way as all the other resizeable columns - by click-and-dragging the right side (see related discussion here).
Since this question has come up on this forum the second time, most likely there are 200 other people, who also had trouble with this, just did not report it, so it would be nice to find a solution that would make things more intuitive and not too hard to implement. Do you have any suggestions?
We could expose this feature to the users with a more convenient GUI, but for now you need to use an sqlite editor if you want to customize the database browser columns.