This would be an unusual thing to see in America, but not in Africa. When I visited Malawi (quite a few years ago) I remember seeing numerous women walking around balancing all kinds of heavy objects (firewood, water containers, etc.) on their heads.
To get good straight stalks of the proper diameter for walking sticks you must strip off the lower leaves at regular intervals. If you get much wind, stake them. The plants are shallow-rooted, like corn, and are easily blown over. Purposely bending the young plants over and then later staking them straight will cause a natural crook in the stalk. This crook then becomes the handle to the walking stick. This type of stick is much prized in England, and fetches a better price than straight sticks.
If the leaves are left on too long the stalk becomes too thick for a proper walking stick and it will often branch out, trying to form limbs. Ideally, you need to remove the lower leaves when the stalk is slightly larger than walking stick size--about 1-1/4 to 1-1/2 inches in diameter. You can expect about 20 pecent shrinkage when dry. I think a diameter of about an inch is ideal for a walking stick...
The specific type of cabbage you need goes by a variety of names: 'cow cabbage,' 'Jersey cabbage,' or 'walking stick cabbage.' And yes, you can eat the leaves of this cabbage.