Escapism, first and foremost. Deliberately so: using the power for good is quickly dismissed with the image of dragons and entire armies being turned to white mice at once. We are never told why the children were sent out to the country, or their father. Their mother works long hours in an office is all we're ever told. The kids are staying with an aunt in Bedfordshire in a small village, they meet a witch, they have adventures which don't go as expected. Unlike the many works of fantasy fiction that have enjoyed a popular revival in film, I can't see this one coming back: one of the only two adventures in The Magic Bedknob is a trip to a South Pacific uninhabited tropical isle that turns out to be populated by a cartoonish stereotype of a tribe of cannibals. They don't have anything that isn't fashioned by hand except an enormous pot to cook in. There is a witch doctor. It's almost too absurd to be insulting.
In Bonfires and Broomsticks the kids are reunited with their friendly witch in the country and they travel back to 1666 London. There is a chap going to be burned for witchcraft, for causing the Great Fire actually, he's a professional necromancer but it's all humbug. Not like Miss Price at all. He holds tremendous respect for her abilities.
It's nice that Miss Price has witchcraft, since she hasn't much else. Her's is a genteel poverty which leaves her plenty of time to do Red Cross work, unspecified. It saddens me to observe that her use of magic makes her a suitable partner for the charlatan, who has a small farm and some gold saved.