The invitation has probably been extended to heads of state only. Heirs such as Haakon will be representing their respective heads of state and not attending in their own right.
Enthronements were traditionally always held in the presence of royal heirs, not sovereigns. We can always watch it in the Netherlands (yes, we had few exceptions at the last one, such as Monaco) or in Britain. In the old days it went that far that Kings and Ex-Kings even being present in town, didn´t attend the enthronement and sent a representative. In the UK for instance this was even extended to own family members as before Queen Mary, who broke the rule, Queen Mothers (titled Majesties themselves) never attended a british coronation.
That´s why it was something unheard of when in 1953 the Duke of Windsor, former monarch of the UK and the Empire, asked permission to attend his niece´s coronation! Of course he was NOT allowed. In the greek royal family there was no one of the royal couple´s children in 1953 over 18 - so Prince George and his wife Marie (Bonaparte) went. It would never had occured to King Haakon to attend the 1953 London coronation (like he didn´t 16 years previous), so Olav, Martha and their unmarried daughter Astrid attended. Sweden: The CP still a small boy, so his uncle Bertil attended. And so on and so on...
And heirs always "represent", that´s nothing new. Such as the monarchs do not attend as a private person, but as representatives of their respective countries.
Kings and Queens normally only attend in modern times when the heir is under aged. In Japan in 1990 there was also a mixture of monarchs and presidents and Crown Princes. So why CPcss Victoria, a middle aged married woman with a respectable consort, does not go to Japan although her parents did the job already 29 years ago and the date set for the ceremony so long known, is beyond me!
The Netherlands: In accordance with tradition the King should have sent brother Constantijn and Princess Laurentien.
Britain: I would have liked to see William an Catherine going to Japan instead of Charles as it slowly becomes a bit embarrassing for him to attend events like these where people much younger come into office he is waiting for so long....
My guess, why he is not accompanied by his wife this time, beside Camilla "not travelling well", is that they want to avoid media comparision of his attendance from 1990 with his 1st wife and pictures of the enthronement with Camilla (such as he could never visit the Taj Mahal with her - or even Camilla alone!).