How do other OSes handle the same functionality without placing machine files in the users filesystem?
They do, however, create their own versions of the recycle bin/trash folder. If you use a flash drive on macOS, Windows and some Linux environments, you'll end up with three different recycle bin/trash folders. A bit annoying, but those folders are usually empty anyway.
Windows warns about the inability to copy permissions to FAT32 (in some cases, at least) and some command line tools on Linux do as well, but it depends on the tool.