Another problem for platform screen doors is that they are tailored for a specific design of rolling stock. So if the ones east of Reading were made to match Crossrail trains with 3 doors per car, nothing else could ever stop at those platforms. And as somebody else said, they require either ATO or an accurate manual stop which adds to platform reoccupation time.
I think the fences that have been installed between fast and slow platforms are all that can realistically be done and I suspect they are as much to prevent accidents as suicides.