The Head of the Commonwealth is the Monarch of the UK and Her/His other Realms and Territories - and not a Politician
Could you imagine the Commonwealth without the Queen as "Head of the Commonwealth"? No one can. Then why is it that such a provocative sentence can be found on the Commonwealth's website:

When the Queen dies or if she abdicates, her heir will not automatically become Head of the Commonwealth. It will be up to the Commonwealth heads of government to decide what they want to do about this symbolic role.
http://www.thecommonwealth.org/Internal/150757/head_of_the_commonwealth/

To say that the "Head of the Commonwealth" is a "non-hereditary position" is science fiction or wishful thinking of some politicians who would like to grab the job for themselves.

When Queen Elizabeth II came to the throne in 1952 she became Head of the Commonwealth and inherited this title from her father, the late King George VI.

To change this tradition would be a revolution, a change of the whole system of how the Commonwealth of Nations works. Should the leaders of the 53 member nations after Her Majesty's death refuse King Charles as new Head of the Commonwealth and elect one out of their own midst, the Commonwealth could end up with a very controversial African leader who happens to find a majority among the members. And I am not talking about someone honourable like Nelson Mandela who is even older than the Queen. And hopefully Robert Mugabe might not be in the race either (at present Zimbabwe is suspended from the Commonwealth). The British Monarch is not only above party lines, but also above nationalism and nepotism.

The Commonwealth with a republican head would be much to the delight of the few British republicans who are desperate to gain some ground, but it would be on the way to decline for lack of unbiased advice from a Monarch.

Look at other associations that were set up by former colonial powers and their colonies. Have you ever heard of the Francophonie, where French speaking countries, not necessarily former French colonies gather once a year to celebrate their language? The Lusitanian Association of the former Portuguese Colonies? The meeting of the former Spanish colonies in South America only gained the public interest because King Juan Carlos of Spain told Hugo Chavez to shut up.

The members of the Commonwealth must ensure the smooth transition of this title after the Queen's death. Her son and heir, Prince Charles, The Prince of Wales, will be a respectable and dynamic successor of Her Majesty also as Head of the Commonwealth with a keen interest in development and measures against climate change.