To save a file, I think (and this is over 25 years ago) I would typically open the Filer window to where I wanted to save the file. Remember this might involve swapping floppy discs.

That would leave me with the Filer window open over the top of the application/document. Middle clicking anywhere on the document wouldn't raise the application's windows over the Filer windows, so dragging the file to the destination was easy.

At the time I preferred it to the Windows 3.1 alternative, which gave you a completely different UI to the general file-browsing tool.

The button on the top left (next to close) on all the application windows is "Send window to back" (of the stack), which would be useful for showing any Filer windows opened earlier.