Nobody can know it for sure as we are talking about future events here. One thing we do know though is that the British care a lot about precedent and, as I said, not styling Harry's children as HRHs during Charles' reign would be unprecedented. Edward's case was already an oddity , but Edward is the monarch's third son, not the second like Andrew or Harry. In fact, assuming Charles is king and William doesn't have any more children, Harry's firstborn will be born fifth in line to the throne. By contrast, Louise was already 8th when she was born , and James is now 10th and Louise 11th.
It just would not happen IMO. Harry would hardly want his children to be treated as less important than they should be in terms of status.
I dont believe that Edward wanted to be an earl, it was problaby a decision taken at the time of low popularity for the RF, in the years after Diana's death.
He was the fourth child and third son, and there were several people ahead of him in the line, so there was only the slimmest possibliity that he woudl ever be king..
that's usually how changes happen.. Firs they happen with the outside people in the RF, usually cousins etc. George V decided to stop the titles going on and on... so that prince Michael's chidlren are merely Lord and Lady First name Windsor.
Minor members of the RF like the Earl of Harewood, got divorces, well before the Monarch's own children were allowed to divorce..
So for Edward to have a lower rank than was usual for a monarch's son on his marriage.. was the way that changes usually happen.
However I believe it also had a lot to do with the fact that in the few years after Diana had died, the RF had had a big blow ot its popularity and they were seen as needing to simplify things and have less ceremony and grandeur and talk about titles and precedence
So Ed was only made Earl of Wessex and his children we were told weren't going to use the titles Prince or Princess. However a door was left open, in that its expected that when Philip goes, Edward will get the title of Duke of Edinburgh and possibly then his children will start to use the Royal titles. At any rate Im sure Edward was not too happy to get a lesser title..
And for Harry who is much higher in the ranking system, to take a lesser title on his marriage or to have his children merely Viscount nad Lady, would be very very unlikely to happen.
He will be the equivalent of the Duke of York, as the monarch's second son. he wont be let off royal duties, and his children will problaby be pulled into them too.
It hasn't happened with Beatrice and Eugenie because there are still plenty of people to do the job, and they aren't very popular because of Fergie and Andrew's own scandals. But they are still HRH and Princesses becuase that's' their birthright as the children of the Queen's second son.