It's possible, but it's also difficult. The strike zone is not a static box; it's relative to the batter. Thus, the umpire needs to be able to compare the location of the pitch to the batter himself, and so the zone should be defined relative to points on the batter.

Currently, the points of reference on the batter are the knees for the bottom and the team letters on the jersey for the top (though technically it's the midpoint between belt and shoulders). These are convenient reference points. Shrinking the strikezone a bit would yield something like "two inches above the knees to 1/3rd the distance from the belt to the shoulder", which would require more explicit rather than subconscious analysis from the ump.