The Queen's health was deteriorating for some time and I wouldn't be surprised if she herself had already destroyed many of her personal papers. Her Majesty - rightly - could not risk having those "accidentally" winding up in the wrong hands."
I would hope that both Anne and Philip would have restrained themselves from such behaviour. I really don't think that the Royal family should be in the business of bowdlerising The Queen's life. If there is a series of torrid love letters from The Queen's alleged paramour, they should be filed (under 'P', perhaps, or 'R', for 'Racing' ).
In addition to Johan's clearly expressed reservations, people today have no idea about what in The Queen's papers might be important a century hence. That is why Princess Beatrice's destruction of some of Queen Victoria's papers is so condemned by historians.
As we saw in the affair of the so-called 'Palace Letters', neither the then Queen nor her advisors were best qualified to determine whether papers were private or public. And as we know from the so-called 'Black Spider Memos', The King is no better placed than was his late mother.
(https://www.theguardian.com/uk-news/2015/may/13/prince-charles-black-spider-memos-lobbying-ministers-tony-blair)
It is also probably worth pointing out that no one is suggesting that all of her papers be put online tomorrow. All of them should be catalogued by the Royal Archivist, another Palace employee but one better qualified than a tall page. We should expect the papers to by closed for, say, a century, with specific exceptions at The King's discretion, for The Queen's official biographer, for example. Normal archival practice, for example, redacting documents to preserve the privacy of third parties would also be followed.
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