The reason--or at least a good reason for this can be found in the delicacy and tenderness Iñárritu lends with filming the eyes of his actors. Whereas filmmakers like Spike Lee and Jonathan Demme trail-blazed such stylistic devices as actors breaking the fourth wall to look directly at the audience, Iñárritu takes his time to build up those infrequent direct gazes at the screen; a big strategy of his is how explicit he is with his cinematic influences. His films Biutiful and The Revenant take certain cues from Andrei Tarkovsky and Terrence Malick, lending a poetic and impressionistic visual prose amidst the overly busy plots--mainly of the former film. His earlier work with Amores Perros and Babel cut back and forth between multiple story lines, much in the spirit of the independent Mexican cinema of that time, but those films too were always grounded in the pathos of the eyes of his characters. Iñárritu definitely sees life as a beautiful chaos--at least in the films he makes--and yet the bravery he emotes comes in still trying to find the tenderness, that special, fleeting, grandeur yearning for human connection and purpose in the midst of tragedy.
And the eyes have it.