But taking a break and taking a walk don't help promote communication between the left and right side of the brain.
Nor do they stimulate different bits of the brain.
A child with ASD, ADHD, Dyspraxia, Dyslexia etc probably has an underdeveloped left cerebellum and right pre-frontal cortex. And probably avoids anything that stimulates them. So they won't naturally get stronger.
So just like a child with poor fine motor skills needs to be encouraged to do activities that use their fine motor skills, children need to be encouraged to do activities that require them to use their cerebellum and pre-frontal cortex.
Doing exercises that require the cerebellum to work could hugely help the child - but it's all very, very hard to measure and to prove.
Studies on programs that take months or years to benefit, and may have any of a number of benefits, are really hard to design. A child's reading may improve, or they may be less anxious, or their social skills may improve, etc. The study becomes really, really hard to design to Ben Goldacre's exacting requirements.
No 'scientific evidence it works' does not necessarily mean it doesn't work. No scientific evidence it works is not the same as 'evidence it does not work'.