Well that's the only thing I can think of to explain your issues. Certainly, item size should not be affecting the tag browser's minimum width (and it does not affect it for me). But its worth checking. And note that it does not have to be a tag it can be an entry in one fo the other categories.
AN easy way to check that is to simply create a new empty library and switch to it, it will not have any tags (or other entries).