It would be nice that when you set ‘Contents are face down’ to ‘Via right-Click menu…’, not only can you see the $BasicName$ but you also have the option to see the top Layer image.
I currently have many force pools (Decks), which contain Counters (Cards) that are face down. When drawing from the force pools, the counters are always face down and remain that way until they are moved to the map. Sometimes it is required to draw a specific unit when certain conditions are met.
Then there is a need to draw a specific counter, or counters based on the values, colors, or symbols, on the top Layer image (Face) of the counter. With over 4000 counters it would take ages to make a separate Trait for each just to do this.
If you look at TabeTopSimulator, you can examine the force pool, which contains all counters face down, and see the face-up image making it selectable.
When selected and drawn, the counter remains face down, you can always flip it later when appropriate.