Well, the answer is that it's sort of possible, not entirely possible, and it's definitely not straightforward.
It didn't work out the way I had hoped ... but in the end I was able to recover.
After poking around my iPhone the only option that appeared to delete all songs was in General > iPhone Storage > Synced Media > Music > All Songs > Edit > Select All > Delete. OK, so I did it.
Oops, well, it deleted all songs that I had imported from CDs over the years ... but it didn't delete any songs that I had purchased via iTunes/Music ... and it left all my playlists intact on the iPhone (all now blank). This is NOT what I wanted. And now, how would I recover?
As I dug into this, everything I found online indicated that if I resynced my iPhone with my Mac, all the songs I had just deleted from the iPhone would in turn be deleted from my Mac! All references I found were to "Apple Music" mentioning "Sync Library" ... and they were totally confusing ... because Apple Music is 1) a service that I DO NOT subscribe to, 2) a Mac app that I DO use and 3) an iOS app that I ALSO use. So, when I sync my iPhone music with my Mac, am I doing "Sync Library" or not?? I did not want to risk erasing all the songs from my Mac.
Eventually, because on my Mac, next to the tickbox under Finder > Music (when an iPhone is connected) it says "Sync music onto <iPhone name>" ... note the word "onto" ... which appears to indicate a one-way transfer (FROM Mac TO iPhone), not two-way sync.
So I took a chance and did the following:
- I made a backup copy of my entire /Music folder on an external drive just in case things didn't work out the way I hoped they would.
- I used the Finder to do a normal sync between my Mac & iPhone including sync'ing music.
Sigh of relief ... all my songs got copied back to the iPhone without disturbing any songs on my Mac. And they were copied back into the correct playlists. The only thing I lost in the process was all the album artwork on my iPhone (it's still on my Mac.)
This "sort of" accomplished what I set out to do, which was to erase & reload all the songs on my iPhone. But it wasn't easy and it was certainly filled with anxiety.