I have wondered if a custom touchscreen setup could be designed to make this easier. The problem seems to me not to be something intrinsically "wrong" with screens, but that the touchscreens are too smooth if you use them with some sort of stylus, and to have too much difference between static and dynamic friction if you use your finger directly on the screen. As an adult, my handwriting gets noticeably worse on a touchscreen with a stylus, and only marginally better than my third-grader's writing when using my finger. It seems like if someone put their mind to it, a touchscreen+stylus combo could be created that would be very similar to pencil-on-paper in feel. It's even possible this could be done with a stylus and a generic overlay that could be put on any existing touchscreen (albeit possibly limited to higher quality capacitive screens).
The disadvantage is that this overlay will probably render the underlying touch screen no longer pleasant to use with a finger, and you probably want a semi-permanent adhesion so it's not going to be a thing you can easily take on and put off. (It could be experimented with but I bet it doesn't work out very well.) But still, an off-the-shelf tablet + $20 (at scale) in stylus + overlay might be able to mitigate and/or eliminate the sensory issues, while retaining the advantages that an app can bring, instant feedback primarily.
(In my opinion, the biggest thing that computers can bring to education is instant feedback, which can be mathematically shown to improve the maximum possible learning rate, and any attempt to bring computers into education that don't involve harnessing this are starting at a severe disadvantage.)
Right now there are two models
A) Web based with ads (Most children activities and games online)
B) Subscription Model (ABC Mouse, iStation)
I would love to figure out another model
I read a lot from our curriculum "Creative Curriculum", accreditation standards and philosophy and my old Developmental Psychology classes. Lots of Academic research and many online resources like the Fred Rodgers Institute (http://www.fredrogerscenter.org/).
The only book I found to be helpful has been "Instructional Technology in Early Childhood: Teaching in the Digital Age." Most books are either surface level practical (I really enjoy the philosophy piece which is usually missing) or outdated and not very valuable.
I can't tell you how many children have difficulty with straight lines vs curved lines. Now bring that to learning letter shapes of A and H or S. It is believed that children learn straight line letters that cross quicker than curved, but I have not seen this with the hundreds of children I see every week. I now struggle on the now what in my work to get down to the shapes sooner rather than later with that work and how to convince these horrible developmentally inappropriate children applications that I use to work more in these foundational steps. If anyone wants to back me to take a 2 year sabbatical to develop some children tools it would be greatly appreciated :)