Why would this be a benefit over the operating system Mac (Bin or Trash) or Windows (Recycle Bin)?
The only benefit I can think of is for open networked files, however, we shouldn't be using networked files anyway due to the increased possibilities of corruption.
If such a feature was added, how would it work? Would there be a File menu item to "Send Active Document to Recycle Folder"? Which would presumably save and close the file and move it to a specified directory on the local disk, removing it from the original location. Perhaps the existing recovery folder could be used?
This could be scripted, but I can't personally see the point.
Adding to what others have said, Photoshop does have its own "Deleted" files, but only if you are saving the newer Cloud versions, .psdc. When you delete a Cloud document, it goes into the Deleted files folder in the CC app and awaits permenant deletion.
As others have said, the older .psd files use the OS Trash/Recycle bins.