Yes, I just noticed that as well...
I took a quick look at the feature enhancements for version 2.1 (coming this summer) and they seem to be focusing a lot on making the whole Projects integration a lot smoother and more robust. Perhaps they will address this as well.
I would not necessarily 'remove' the project since I think that deletes all references to the project and I would not be able to go back and check recently finished projects for info. I would just 'hide' it from the dropdown list.
I have the add-in set to delete completed items every 14 days... I imagine that deleting the completed projects would remove them from both the drop down list and the project management page.
I guess I'll find out the next time an 'auto-delete' rolls around.