I just bought a panel to make one!
I'm like you and while they don't talk about quilting ... I'd want to!
Outline Quilting around the characters would be one way, although, the backside of the page, the character isn;t there and it wouldn't look right. So a meander or stipple, might make more sense.
The other thing I'm contemplating, is splitting the pages, and the backside of each page use prints that go with the book. Eg. the one I have is all about farm animals and the sounds they make, so I thought, for the horse, then I'd use a print with horses, etc. This way you could quilting around a character and it wouldn't matter to the all over print.
In the one store they had one made with poly batting, and it was too puffy for my liking. Another store had used fusable fleece/batting. When I shared my idea, the lady suggested just using flannelette.