>Think about doctors walking around healing people, doing surgeries. That's basically what a witch does. Where else do they get their power?

Healers in the middle ages performed life saving surgeries, even on people with serious injuries to their skulls. (This isn't supposed to be a scientific defense of medieval healing techniques, but these were skilled people with limited tools and knoledge trying their best. Same as today.) Successfull healers weren't considered witches, because they were recognized as a legitimite profession and the catholic church largely regarded "healing magic" as pagan superstition.