Great suggestion. We've actually been considering this as of late. The idea is to take the ability to customize a space/project/homepage to the next level by adding in additional places that content can come from.
In the meantime you could probably write a pretty simple widget to make this happen. I figure it'd have one property -- the ID of the document to display. Only one gotcha to be aware of would be permissions: you'd need to code the widget to handle the case where the viewer of the content doesn't have permission to see it. Probably easy enough to just have a simple "you don't have permission to see this" message.