Another option until Apple gives us a better one:
If, like me, you have your additional desktops arranged just how you like them, then the thought of deleting and recreating them just to change the wallpaper would be like recommending that I demolish my house so that I can repaint the walls. I'm not going to do that.
Instead, you can open up your Desktop preferences ( > System Preferences... > Desktop & Screen Saver ), then change the wallpaper on the current desktop.
Then, open Mission Control (on my machine, I launch Mission Control with the "Swipe up with three fingers" gesture) and drag & drop the Desktop & Screen Saver window onto the next desktop. The window will update to reflect the new desktop in focus and I can switch that desktop's image to whatever I want it to be. Repeat for as many desktops as you have. (If you have multiple monitors, then each monitor will have it's own Desktop window, named something like "Secondary Desktop".)
This is a lot easier than closing and reopening the desktop preferences on each desktop, and way easier than deleting and recreating all desktops (for me, at least).