Wonderstuff I remember that research too.
In my experience a lot of the trouble is harassed teacher gets TA to do worksheets with the lower literacy group during assembly, but no one checks if progress is being made.
Teacher takes longer to realise DD1 still can't read or spell than if she'd taken that group sometimes. (DD1 is very articulate and happily answers questions in class, not a child who'd strike you as not learning to read until Y6).
This is partly the teachers fault for complacently thinking DD1 is getting help and partly the TAs fault for not reflecting on her efforts.
Mainly it's the fault of a system that doesn't give time for teachers and TAs to talk and TAs the training to be confident in recognising and raising concerns.
Inevitably TAs are going to get dyslexic, dyspraxic and similar children in their groups, they need training in how to help them.