Henry... the left-right "reversal" to which you refer occurs
ubiquitously within mammalian nervous systems for one reason...
The nerve-fiber termination distributions that result align with the
totally-inhibitory outputs of the cerebellum so that the problem of
activating the muscles to move away from environmental sources of
noxious stimulation can be resolved by "simply" minimizing the
topologically-distributed ratios of excitation to inhibition (TD E/I)
occurring within the neural architecture...
This pain-avoidance problem is infinitely-large in scope... yet this
"simple" neuroanatomical solution typically resolves it in millisecond
time frame... so this neuroanatomy-based problem-solving strategy has
extraordinary survival value...
The anatomical antecedants of the the bilateral crossing phenomenon
("decussation") can be traced all the way back to organisms exhibiting
radial symmetry... coelenterata... jellyfish...
BTW, I've developed a theory of nervous system function that traces such
neural architecture throughout the entire CNS... the
information-processing significance of the fiber crossings extends
strongly all the way into the highest-"level" realms of cognition...
ken collins