Similar to mine too. Though my 'Desktop' is my Google Drive folder, always sync to cloud. My real desktop though, is temporary place for pile of files of current working project of that day. I clean up this real desktop at the end of the day, put the files into their rightful place or delete it, just some old habit.
I have some kind of 'shelf' too, but your idea about taking element from soon-to-archive project and put it in a shelf is what I overlook. I'll give it a try!
It can be hard to separate things in the beginning because if you ask yourself: "What is important from this work that should be in shelf?", your answer would tend to be "everything". So, instead, you should be asking yourself "which elements can I be reusing in future work?" regardless of their importance.
I have some kind of 'shelf' too, but your idea about taking element from soon-to-archive project and put it in a shelf is what I overlook. I'll give it a try!