The American series (House and Elementary) has the advantage of more seasons and episodes, which I think is sometimes required to showcase the challenges of drug addiction and mental health.
The fact that these characters having to come back to face the same problem over and over again episode after episode is more true to the nature of the mental health problem itself.
BBC Sherlock has too little episodes to bring audience along a prolonged struggle with mental health.
It's definitely one of those pieces of media that is extremely frustrating because of how close it came to being an all-time great adaptation. Moffat needed somebody in the writers room with him to tell him 'no' sometimes.
