Even in girls schools where corporal punishment was in use, or co-educational schools where it was used with girls, it was far more likely that it was seen as a last resort to be tried only in cases where other methods weren’t working. When they worked (as they normally did) you didn’t need to try it. In boys schools, the cane was often used much earlier on, and because it worked so often, schools tried other methods only when it had failed. Mid level (or sometimes first response) strategy with boys – last resort with girls.
If boys schools had no cane policies then other punishments could be just as effective,
Did tradition play a part? Certainly – but most traditions in schools actually have some common sense behind them at least originally.