Answered by Alex Beam:
The 72 hours is a legal construct deriving from our tradition of habeas corpus -- a judge does not want to incarcerate any citizen witout due process.
As I understand it, the purpose of the "three-day" is to provide time to find a psychiatrist, or family member -- preferably both -- who will either commit the patient involuntarily, or plead for his/her release. This is not a decision that a judge wants to make alone.
As to the second part of your question, good systems DO assign social workers to follow patients after release, and to help the family with care. The newspaper for which I work, the Boston Globe, tells us today that the state legislature here plans to cut $60 million from mental health care funds, some of which undoubtedly pay for "extras" like social work follow up.