Thank you for posting. It's a great request and one that I will share with our engineers for further review.
A helpful feature to be aware of is the Send To integration in TheBrain. This will only work when moving a file from a Windows Explorer window. When you right-click a file or folder in Windows Explorer and select the Send to PersonalBrain command, that file will either be saved as an attachment on your home Thought or on the current active Thought (specified in the Preverences > UI window in TheBrain). So you might be able to save a bit of time by setting up the desired destination location in your Brain settings, then saving from the Web to your desktop and use the Brain's Send To integration.
Also, feel free to post new feature requests (or vote on existing ones) at http://thebrain.uservoice.com.
Our engineering and design teams often visit this site to see what popular requests are being made.