I think the problem is that too many "researchers" today use only the internet - where we know the same stuff gets repeated over and over.
The details are together here, in the hope that some future researchers might land here
and go to the sources.
Philip's dukedom was hereditary - see pic below of the entry in the London Gazette - "heirs male of his body lawfully begotten".
Charles was the heir and inherited.
The Wessex agreement said the title was to be
given after the title
eventually reverted to the crown.
Quoting the announcement from BP -
" Saturday 19 June 1999 00:00
Buckingham Palace (National)
TITLE OF HRH THE PRINCE EDWARD
The Queen has today been pleased to confer an Earldom on The Prince Edward. His titles will be Earl of Wessex and Viscount Severn. The Prince Edward thus becomes His Royal Highness The Earl of Wessex and Miss Sophie Rhys-Jones on marriage will become Her Royal Highness The Countess of Wessex.
The Queen, The Duke of Edinburgh and The Prince of Wales have also agreed that The Prince Edward should be given the Dukedom of Edinburgh in due course, when the present title now held by Prince Philip eventually reverts to the Crown.
The Queen has also decided, with the agreement of The Prince Edward and Miss Rhys-Jones, that any children they might have should not be given the style His or Her Royal Highness, but would have courtesy titles as sons or daughters of an Earl.
To be released at 12 noon BST Saturday 19th June, 1999. "