Hi Andrew … there isn't a way to automate this, unfortunately. I will consider enhancements along those lines for a future update.
In the meantime you might find it at least a bit more streamlined to use the Media Manager to locate and select your images for insertion. It includes the same kind of configuration stuff as in the Upload Utility, but if you just select and double click an image in there, it will be attached to the post automatically as you describe.
Note that you can add custom folders to the Media Manager sources list so if the images you are uploading are usually from a specific spot this might be a good solution.