I don't believe King Charles will live along as the late Queen. So his window of opportunity for his Kingship is limited.
The fact that he so swiftly made William Prince of Wales speaks volumes. He should imo, fulfill his parents wishes and give the Wessexes the promised Duchy of Edinburgh. That's a quick fix. As mentioned before it will cause King Charles nothing.
LOL... Now that the Edinburgh-title is merged with the Crown, any king can recreate it. If poor Charles does not survive his mother's funeral (as you seem to imply on hurrying him up before his mother is even buried), the next king William could create his uncle as "duke of Edinburgh". I personally don't see any need to hurry before the funeral and mourning is over and a bit of time has gone on. I don't actually see the queen leaving Letters Patent for the title to her eldest son to sign as soon as the title merged with the Crown (and he thus lost it!). Now that would be shabby to the first Duke of Edinburgh, to his eldest son and to the son the queen and the Duke wanted the title to go.
Another question: will the Duke of York remarry his fomrer wife now? Would she have him again? Advantage in case of a remarriage would be that "The Duke and Duchess of York" could hope for the forgetfulness of the public with all those new titles in the new reign and go on to live like they want (as long as they do it quietly... At least that would be king Charles' wish I guess)
Another thought: I am guessing Charles never thought about doing something to remove the gift of the title/style of HRH, Prince/ess of X from the grandchildren of a monarch because that would have left dear queen Victoria without a Royal title from birth, even though she was the heiress presumptive of her uncle (and wasn't Elizabeth II. born when her grandfather was king, so this would have left her without a Royal title as well?). When the late queen couldn't stand the idea that the heir's heir's children wouzld be without a Royal title? Though I guess he will leave it to William to supply his daughter Charlotte with a title of her choice. But maybe she would prefer The Princess Royal once Anne is dead (and buried!!!) or marrying a peer, so she could become HRH Princess Charlotte, the...(Lady, Viscountess....) Z.
Though when we discuss (not sure if we did it anywhere yet) that if parliament had upheld the Third Succession Act (including the right of the king to will the throne to any relative) and later King Henry VIII's will and testament (which put the line of his sister Mary before that of her elder sister Margaret) amd the marriage of Lady Katherine Grey to Edward Seymour wasn't illegitimate (it only was because of Elizabeth I. political reasons), then the currant queen of England would be Teresa, 13th Lady Kinloss (a Scottish title, btw). So...
Let's be glad all happened because the English parliament realised that it would be better for both kingdoms to have the same king or queen and offered the throne to James VL. of Scotland, the heir in the unchanged (so more common line of inheritance) via the elder sister Margaret and then that they decided to give the throne to a smaller Protestant German dynasty which was safe and established when the alternative to the Protestant Stuarts were the Catholic Stuarts. It so makes sense!
And finally, when those "male-line, real blood Stuarts" had died out, why switch (again) to an Italian which was involved in internal wars back then? Plus the fact that the "Jacobite heir" had just (5 years ago) renounced his claims to his own throne, had no children from his marriage to the sister of guilliotinated king Louis XVI.of France) but hadin the beginning of the revolution been forced to held up the treaties he had made with his brother-in-law, so was actively involved in the first revolutionary wars till his abdication! While his brother, the next king, was disposed by Napoleon- And both never even claimed the Uk-throne!
While the "Georges" were already established and had enough children to fill in a line of succession with male heirs from the male line? Well, at that time it was an "heiress presumptive" to the Prince of Wales but after he were some male heirs (till it became queen Victoria ....you get what I mean here? And the Uk fighting off Napoleon?
So for me it makes sense that Charles is now "king Charles III", that there was no "Charles III." before him (even though lawfully Bonnie Prince Charles would have been that) and seeing as the kind does (he has an academic degree as an Historian after all!), all is well (for me) as it is. And will be once Charles had time to bury his "Darling Mama" together with his Darling wife, Queen Camilla.