I guess she said 'Duck Rabbit' at the end because that's the name of the book?!
I think they complicated the issue by having it do two things at once.
Ostensibly, it's part of a series, #savebystories, where celebrities read children's books to the camera. So you can watch with your child. Showing the book to the camera and reading to the audience is therefore integral to that.
Although Meghan said something about reading for save by stories at the beginning, it would have worked more in her favour if she'd made it clearer what save by stories was briefly, and that it was a series and not a one-off she was doing.
That would have helped the audience to know that of course she had to show the book to the camera, thus avoiding that bit of criticism. All the other celebrities doing this show the book to the camera much more than Meghan does, because they don't have a wriggling baby on their lap.
By making it also about 'celebrating' Archie's birthday and showing him off, it meant that a lot of people are only watching it for that and only seeing it through that perspective.
It was always going to be really hard to do both successfully with a child that young. As a PP suggested, it might have worked better if Harry had held Archie so Meghan could concentrate on reading for the camera.
I said above I thought it was endearing. But if their two aims had been separated out, people might have been a lot clearer about what the intention was and therefore less likely to criticise because they weren't quite seeing it for what it was.