I agree with @belleager , they're taking the short term pain for long term pain and drawing a very reasonable boundary about their private lives. They have decades of this shit ahead of them.
I don't know that there's anything actually new here, I don't think Kate's ever discussed her HG to any real extent, don't think we know if she breastfed, there's a scar on her head from "surgery as a child" but nothing else has been said on that either. I'm sure there are other examples.
The whole "just release a photo of her reading cards" thing confuses me. Have you seen the level of scrutiny in this woman's appearance? She can't just snap something on her phone.
She would have to sit still long enough for a blow dry, which would probably be uncomfortable. Her extensions probably need attention, again uncomfortable. Abdominal surgery means weight loss more often than not and she didn't have any to lose so she probably is looking a bit gaunt and generally not at her best aesthetically and make up wouldn't hide that.
The clothes choice would be analysed, the usual who's she wearing but also do the clothes hint at the surgery. The background of the photo would be analysed as we don't tend to see inside their homes, but at least she wouldn't have to do the tidying.
She prefers to take the children's photos herself and so control the images released (I think this was a stroke of genius tbh) so they probably wouldn't be in the photo but then the internet crazies would quickly turn to WHERE ARE THE CHILDREN?! THERE'S SOMETHING WRONG WITH THE CHILDREN!!!!!
She's right to say as little as possible. I'm sure she'll show up for church on Easter Sunday looking more or less the same and then hopefully the speculation will calm down.