A pathologist will not touch a cadavar unless a Life Extinct document has been issued and an order to Conduct a Post Mortem.
In the case of a Medical Practitioner examining the deceased they may be satisfied the person died of Natural Causes and is happy to issue a Death Certificate stating his reasons (ie having had recently seen or been treating the deceased for a disease(s). The Police are then requested to contact the family for more supporting evidence ie medications, witnesses etc and are then asked if they now request a Post Mortem be conducted, sometimes at the families expense.
In the case of Sudden Death, the cause of which is not known, then an Autopsy is compulsory to establish the exact cause of death, even though it may appear obvious, together with any other mitigating circumstances, ie inteference, medications etc.
The rest of the process follows suit as you explain.