To do with the properties of the wood isnt it. To cure infection...down there...
What is interesting is how that was twisted with no doubt some individual claiming he/she saw that person flying about on it, which has led to the idea of witches and broomsticks, when the true of it is a medicinal herbology cure.
Another interesting line on the was that is twisted to brand someone a witch in the middle ages is the was the Pantomime Aladdin is racist, or bigoted rather.
The magician - of middle eastern origin, flies about on a magic carpet.
This idea is also middle age in its origin, and again stems from some hate filled individual claiming he saw an Arab, or follower of Islam, on a carpet flying about, so must be 'of the devil' and ripe for burning at the stake.
Coincidental that the carpet is in fact a prayer mat ?
Always found it funny that that seemingly innocent characterisation is lost on the average panto goer.