There cannot realistically be any suggestion that HM should be followed by anyone other than Charles, and after him William. No one with a really high public profile across the world would exactly be lining up for it. Equally, a former PM of Australia or Pakistan or Barbados etc. etc. would simply not be able to bring to the organisation the kind of PR it needs to justify its existence.
Say what you like about the Commonwealth, the BRF play an enormous role in keeping it relevant. I suspect that, if you take away that personal connection, something would be lost from it. It's doing good things across a whole range of sectors and it would be sad to see it diminished.
I think the problem with it being anyone other than Charles, William etc, is that it risks turning the position into a political position and therefore would lack the ability to unify an organisation of very, very diverse nations.
For example, if it were a rotating position between heads of government, there is no way Margaret Thatcher could have been acceptable to African and Caribbean nations given her position on sanctions against South Africa. Likewise some heads of state/governmanet may be considered to have unacceptable human rights records.
We only have to see from the choice of Olympic and football world cup venues how non-political decisions can become geo-political rows or open to bribery. What should be a simple decision based on who is best for the job, has the potential to become divisive.
I can understand the argument that Charles will only be monarch of a limited number of countries in the commonwealth (and William and George probably even fewer) and therefore why should he be head of the commonwealth. There is too, the uncomfortable reminder of Britain's colonial past. I am also generally predisposed against inherited titles and positions but, in this case, I genuinely believe the King or Queen is best placed to be the unifying force. Charles has spent his life visiting commonwealth countries and William and George will do the same over their lives. Who else would have had the contact with all the commonwealth countries that they will.