The cane across the bottom seems far more humane compared to getting it across the hand so why was bending over considered in many schools to be the way you were punished for the most serious offences. I would say it should have been the other way around!
Of course the strap/belt used in Scotland (and other odd places in England) has the same problem but seemed to have worked
Caning on the hands, dangerous for the reasons you outline above, was preferred by some teachers who were aware of the sexual implications of bottom caning.