This is one of the two things that I can see happening with Edinburgh, and which would explain Edward’s ‘pipe dream of my father’s’ comments. At the time of the original agreement, it wasn’t known that succession would be gender neutral within 15 years to eventually create a purpose for the Dukedom of Edinburgh in this way, that would honour both the late Queen and the late DoE as they were the first.
It’s a little odd that the Duke of Edinburgh awards are run by someone who isn’t the DoE when the title is available, but the moment it is given to Edward, it will eventually go to James rather than someone closer to the throne. They will be aware of the Dukedoms that are soon to be non-royal and in time, that would happen to Edinburgh under the original plans (unless of course it is a lifetime only grant to Edward, after which it would be available for use by future consorts.) Of course the future consorts won’t (or are very unlikely to be) descendants of Philip’s so there would be a need to acknowledge they were going against his wishes to a degree.
My other thought was Louis. There is a role for a firstborn and a daughter, monarch and Princess Royal, but nothing for a second son as such (as said above, there are a lot of Dukes, so it’s not as special a title/role.) Giving Louis DoE instead would be a prestigious role for him rather than wondering what to do with him. Philip made DoE his own but not everybody granted a Dukedom would be able to build something up from scratch; also with the Queen’s children, there were two without roles as such (Andrew and Edward,) while it seems that Louis will be alone in that, as Harry was. If DoE goes to Louis, it still continues among Philip’s descendants. Wessex, as highlighted probably means more to Edward to pass down himself. If DoE were created exactly as before, he would probably feel it should go to Louise given her bond with the late DoE, but she would be ineligible despite being the eldest. Ultimately they were brought up without the expectation of a Royal role, so he probably thinks it’s best not to burden either of his children with it. Whoever is the next DoE, they’ve got big shoes to fill.