Timeline of Carpet and Broomstick AvionicsSteve Vander Ark
Sylviana the Sleek gets the cool idea of making her regular old Muggle broom fly as a way to get to Diagon Alley in a hurry one Friday morning when she ran out of dragon spleen. She finds the ride curiously enjoyable.
Flying brooms catch on in a big way amongst witches; wizards refuse to try them because, well, it just looks like it would hurt.
Muggles all over the world start to get suspicious as more and more witches are flying all over the countyside, sometimes with no particular place to go; broom accidents are more and more common since the enchanted Muggle brooms offer no protection for the rider in the case of collision or just losing one's grip in a moment of particular enjoyment.
Wizards are beginning to get jealous of their womenfolk, but there's no way they're going to ride one of those things, so Bubba Bathless, in the midst of a late-night gripe session with his closest mead-drinking buddies, hits upon the idea of making the carpet they happened to be almost passed out on fly, which means he can recline and drink mulled mead while he travels around. He can also do so with his friends. This idea is embraced wholeheartedly by the wizards and disdained by witches, who find brooms so much more, I don't know, gratifying.
Flying carpets become even more popular than brooms, and huge parties are held in midair as wizards discover that when they congregate on a huge carpet they can 1) carry munchies and mead in vast quantities, 2) hide the fact that there are a bunch of Witches of Ill Repute aboard, and 3) hide the whole thing from their wives.
Witches, who are inventive and innovative, create better and better brooms. Wizards, who are just having a great time so leave well enough alone, confine their innovations to constructing larger mead coolers, adding fluffier cushions, and using fabric that is easier to get the unidentified stains out of so the wife doesn't ask too many questions.
Magic flying brooms begin to replace the old enchanted Muggle kind; these are specially constructed with charms to keep flyers on them just so, and Muggle-Repelling Charms that make Muggles just think they see a particularly large goose flying by. Many jokes crop up about so-and-so's wife being a goose. These jokes are told mostly on flying carpets amongst Wizards and their "guests." Muggles meanwhile are reporting stange things falling from the sky, including empty bottles and women's underwear in unlikely colors such as emerald green and peacock blue.
Something must be done. When Agnes Granitebiter becomes Minister for Magic, she takes stern action. She sets up a commission to oversee the development of brooms that can be safely ridden by all witches and wizards and bans the enchantment of Muggle brooms and carpets entirely. Especially carpets.
Magical brooms become the standard form of personal transport in the wizarding world. Many fond, wistful stories are told of carpets we "used to have" and the wonderful, wholesome adventures of long ago. Great-great-Grandma witches still snort into their elderflower wine when these stories are told. Great-great-grandpa wizards still get a strange light in their eyes and perk up suddenly when these stories are told.
Carpets are still enchanted secretly over the years and for sufficient Galleons, one can still get invited to an illicit "Carpet Party" over London. The word on the street is "Check with Crabbe" if you want in on the deal.