Done your survey. If you price right it would be good. As others have said if you can link to learning whilst being fun then the child will enjoy (luckily my 4 year old loves sitting down and learning maths, reading, writing with the books I have purchased).
I do agree that she (like others) is highly iPad literate and loves the apps and instant gratification this can bring, but as another parent has stated she is limited to time on this and nearly all her books are printed media with cbeebies games etc used on the iPad. But, as others have suggested, offering something different, building the excitement with them 'when is your next story/letter going to come', 'are you looking for forward to your next 'insert character name' story' etc definitely gives them something different.
Remember children do not (in general) get post, and to them it is an exciting thing that only mummies and daddies do. Also you are not competing against a saturated market, you are offering something different and a different experience to the child.
I think it is a good idea, I might be cheap, but selected the lower pricing option. You have put them as weekly costs, but most people work on monthly budgets, when converting to monthly (and as someone earlier stated you are not getting the instant reward) then 15-20 quid plus a month starts to become an additional expense that may not be required (even though I would probably spend a lot more than this a month on new books, but as they are more an impulse buy and you are selecting what you want to buy them, it is different).
I think it will work as a business, but think you will keep customers probably 6 months, before this new experience of receiving the letters wears off (unless the stories are on Harry Potter level and the kids really want to know what happens to xxxxx next week, maybe have a few 'cliff-hangers' for the pester power from the kids to keep subscriptions going). If that works for your model then I think you could do well from it, as there will always be new children hitting your target age, but then that means you have to continually market your product to attract new customers, as I do not believe it will be something someone will keep from 3-8 for example.