The reason it isn't working is because the file isn't called DownloadsIcon
the icon for Downloads is just called Download, but with spaces so you need to do
cd ~/Downloads
touch -mt 202001010101.01 " Download "
That is why you are getting a blank file called DownloadsIcon, because the touch command creates the supplied file if it doesn't exist.
You don't need to touch the icons for other stacks unless you have them sorted by modified date also. However there is a problem with this whole thing...
If you have it set to date modified rather than date added the download stack won't work correctly. Safari saves the file with the modified date the server sends in the header, and so the latest download won't always appear at the front (or just behind the tray icon). For example I just downloaded PhpDocumentor which has a last modified date of "Monday, 23 July 2007" and so it doesn't appear in the downloads stack fan view at all because it is older than other downloads.

Can't seem to find a way to set the "added" date on the icon rather than the modified date, I'm assuming this is some HFS attribute as I don't think the touch command can do that