The system was never designed to do what you want it to do.
Copying music between a computer and an iPod nano was always one-way: from a Mac or a Windows PC, to an iPod nano. You could only synchronize an iPod nano against one computer at a time: if you synchronized it with another computer or library, that wiped all of the music loaded previously.
In addition, the iPod did not store the music out "in the open" where you could copy it off by treating the iPod as a USB flash drive. The idea was that you safeguarded the iTunes library (now the Music library) on your Mac (or PC) by making and keeping backups of it. If you got a new iPod (either because you upgraded, or because something bad happened to the old one), you would load it from the library that you were keeping safe on your computer.
There may have been technical reasons behind some of this, but it is likely that this was also a sop to the recording industry.