Not to mention that in particularly sick patients problems tend to compound one another and exams are often requested to deal with a particular side of the problem, ignoring, perhaps, the major (but already known and diagnosed) problem etc.
Often times factors specific to a hospital play crucial role: eg. in hospitals for rich (but older) patients it may be common to take chest X-rays in a sited position (s.a. not to discomfort the valuable patients...) whereas in poorer hospitals siting position would indicate some kind of a problem (i.e. the patient couldn't stand for whatever reason).
That's not to say that automatic image reading is worthless: radiologists are, perhaps, one of the most overbooked specialists in any hospital, and are getting even more overbooked because other specialists tend to be afraid to diagnose w/o imaging / are over-reliant on imaging. From talking to someone who worked as a clinical radiologist: most images are never red. So, if an automated system could identify images requiring human attention, that'd be already a huge leap.