To be fair to the RF, They did give Diana a state funeral, which is why it needed the pomp and circumstance, and the walking behind the coffin etc. She could have just had a private ceremony somewhere.
And William was 15, an age where it might have been good for him to say goodbye to his mum at an organised funeral. The idea of the state funeral is to honour and show respect for the person who has just died. I think it would have been worse for the boys if they hadnt been invited and included in their mothers funeral, to be honest. They werent small small children. it is a bit damned if you do, and damned if you dont, kind of logic! If the boys hadnt gone to the funeral, it would also have been traumatic, because the felt excluded from something so personal!
It was the death of Diana itself that was traumatic for the boys. not really the funeral or aftermath. But it was 25 years ago. I would have expected both of them to have reached some kind of maturity and peace with it by now!