"Non-lucid dreams are, for all intents and purposes, psychotic episodes. Trying to DILD is like a schizophrenic trying to cure himself spontaneously during his own pyschosis. It can happen, but you're starting from a position of weakness"

schizophrenia is a mental disorder characterized by a breakdown of thought processes and by poor emotional responsiveness. Common symptoms include auditory hallucinations, paranoid or bizarre delusions, or disorganized speech and thinking, and it is accompanied by significant social or occupational dysfunction - wikipedia

Your comparison is weak, waking in a dream and curing your schizophrenia is definetaly not the same. A schizophrenic patient is usually delusional and lives in false reality of which he is convinced is true. A dream however is founded upon our walking life and expectations. With intent it is easy to teach the brain how to spot that it is a dream, there is no self imposed barrier like paranoia or delusion which stops us from questioning our reality. Through the use of prospective memory we can remember to question reality when we are in our dream. You make it sound as if we are mindless idiots in a non-lucid, on the contrary we are just representations of our walking life. Therefore whatever you do in walking life can be reflected into a dream.