Categories would be a much more complicated feature. One that would probably require data about the image (i.e. the category) being stored in a database like MySQL. That introduces lots of portability issues between different blog software. The ability of use subdirectories would be really very simple and would allow you to implement any number of different categorization schemes. You could categorize by subject as it seems you are desiring, or you could categorize by date, as I am wanting. All that would really be necessary is an additional input area to either rename or extend the path to the subdirectory where you want the file to reside. I don't believe there would be any security issues because you can set the topmost level with the current options.
I trying to understand your concern with the "title" attribute. It's nearly the same thing as the "alt" attribute. And it seems to make much more sense to include it since when you're uploading an image it asks for a description anyway. To not include the title attribute means that the only time you actually get to see that description is when the image fails to load properly. That is what "alt" is for. The correct usage of a description is with the "title" attribute. What's more, if you look at the code in upload.php you'll see that they include the "title"attribute if it's creating a link to a document, but not if it's an image. It would be trivial to add this feature. It doesn't need a plugin. This is just basic stuff that should be there. Maybe it would be better to provide an option page that allows you to completely customize the html produced when an image is uploaded. For example, ideally, I'd also like the width and height of the image plus whether there should be a border or not included in the produced html. Plus, if you created a thumbnail, most likely you did so to use as a link to the larger image, the generated html should reflect this. It seems as though image uploading is still very simplistic in WordPress. I've only been using it for a couple of months, is this a relatively new feature?