Precomps with unique instances
Have a composition containing many layers and properties (a chest of toys)
Bring that composition as a layer (precomp) into a main comp (room)
Have a controller on that precomp layer that affects the contents of the precomp (a knob on the outside of the chest that changes the toys' colors)
There are plenty of cases where this would be useful.
One advantage of precomps is being able to have many instances (as layers) in a main comp or multiple comps, and being able to update all instances by changing the precomp. Great.
If each instance needs to be slightly different, however, the precomp must be duplicated so that each instance can be different. Now the advantage of updating one precomp and reflecting change across all instances is lost.
(One workaround is changing properties across a precomp's time, which can be remapped from its layer in a main comp. Obviously not a solution with animations present in the precomp.)
The problem is that expressions within a precomp cannot know what composition the precomp is nested in. It cannot reference instances of itself (the precomp's layer in a main comp) because it would return different values depending on the instance. But that's the point - that would be a great feature to have.
What you describe is possible, as of the April 2018 update to After Effects CC (version 15.1), using the new Master Properties feature.
Details about how to use Master Properties are here: