I am really not surprised by the lack of photos. Just like we never get to see snaps of the children at their extracurriculars, the drop offs/pick ups (only when it suits their parents as there were I think two times when photos emerged), at birthday parties and so on.
Kate will very probably only go to where she is sure she will be left alone.
I mean, we never see pictures of Archie and Lili- doesn’t mean they don’t exist or are locked up at home. People are just not as crazy about „celebrities“ anymore as they used to be. Sometimes there is a peak but it goes by rather quickly. I believe we are so over exposed that it’s just not as important anymore. W&K entertain an especially boring image- so it’s not as if there is much to see anyway. The UK media will act all high and mighty and above such lowly intrusions. They have their own agenda. The UK citizens are never as intensely interested in their royals anyway. And who would fly over to stake out to hopefully they get a photo? Being a paparazzo is not as lucrative anymore. And there are laws, so if you are a ordinary individual you could get in trouble if you sell those images.
This whole „where is Kate“ is happening in a pretty small bubble. Royal watching as a hobby is mostly met with patronising eye roles. We got used to not see her for long periods of time when she was completely fine. So half a year/year when she is seriously ill is not surprising at all.