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chikki Sorry but that hypothesis doesn't fit the facts. If they honestly thought the cane was effective, why did they exempt girls? As you say, if it worked, why change it? If the girls were well behaved despite not being liable to be caned, obviously the cane was not only ineffective, it was probably counter-productive. Again, as you say, in some mixed schools (mine for example) girls were caned so there was obviously no reason for them to be exempt. The cane was also widely used in girls' schools.
In my experience, parents tended to be more egalitarian too so girls were subject to CP in the home, just like their brothers.
It's possible that some teachers used CP for sexual gratification even in schools where boys and girls were both subject to it but it's more likely they believed CP was necessary to maintain discipline. They could not have honestly believed that if they automatically exempted half the students no matter how badly behaved they were.