Because witches are compulsive clean freaks. Whenever you see one flying on a broom, you can be sure she's heading to her next cleaning job.<br />
If brooms didn't exist, I expect you'd see modern witches riding carpet steamers and electric dishwashers (for really big witches who don't know any diet spells). ;-)
They're eco friendly, ergonomic and get good gas mileage
Seriously it was because they used a broom for fornication and put a drug on the end of the broomstick. That's why they felt like they were flying, it was hallucinations.