I think people were wondering where she was because certain elements on social media were doing their best to conspiracy theorize in order to damage the Wales family because they hate William and Kate. You don't make a 30 series Tiktok series called Where the F* is Kate Middleton, speculating darkly about William, out of genuine and compassionate concern; you do it because you have an axe to grind or you're making a significant amount of money, or both.
Were most of the social media posts from low-information non-royal-watchers who have no idea about how the Palace works but found the speculation interesting or compelling? Yes.. I saw them myself (and ground my teeth a lot because holy hell, people who have no idea about the institution are not making useful contributions to the conversation).
But that conversation was *driven* by a cadre of social media users who've been driving the Anti-Kate/Anti-William narrative for years now. And those people would not stop spreading their poison; if the Palace had photocopied 3 million copies of her surgical and path reports and flown over London shovelling them out of the back of the plane, the cadre would spin the details ("they're fake, you can tell from this sign" "it's just an attempt to distract from the "affair") or outright lie, the same way they've been doing all along.
It's one thing to fight misinformation, which is hard enough. Fighting disinformation is effectively impossible, especially when people are highly motivated to spread it. I cannot blame Kate for not wanting to offer up her private medical details, or "proof of life" videos just to have them weaponized against her by malevolent Twitter, Insta, and Tiktok harpies.
In short, it's easy to say Kensington Palace could have done it better, but I honestly don't think it would have made much difference to the online cruelty, and it would have set toxic expectations for the future.