Would the way to counter this be using a default / well-known wallpaper? You'd have the same the wallpaper "ID" as several others who stick to the default wallpaper.
That, and/or change your wallpaper relatively frequently. There seem to be apps that can automate changing your wallpaper, including an official Google one.
Changing your wallpaper frequently doesn't reduce fingerprinting. Each new wallpaper is a new data point for fingerprinting. The timestamps of wallpaper changes are also data points.
The only way to thwart fingerprinting is to make the data points the same on most devices. If you're changing the wallpaper, then it must change in sync with the other devices. Leaving the wallpaper at the default is simpler.