One thing I have to wonder about the SMB2 carpets is why the Pidgits are able to ride on them indefinitely, but your characters only get a few seconds on them before they disappear. Is it a weight issue, or do they have some sort of self-destruct feature for when someone other than their rightful owner uses them? Pidgits reappeared in a few other Mario games, but only occasionally did they use their carpets. If you can beat the Special World in Super Mario World, the Bullet Bills all turn into Pidgit Bills. Pidgits didn't appear that much in the Super Mario Bros. Super Show cartoons, but there was an episode in which they ate carpets instead of riding them. Was the fact-checker who'd actually played the Mario games on vacation at the time? Actually, though, it might be convenient to occasionally take a bite out of your means of transportation. I suppose you wouldn't get much of a trade-in value for it after that, though.
Magic carpets appear in a lot of different fantasy stories, but they're most closely associated with the tales of the Arabian Nights, and most specifically with the story of Prince Husain's carpet. Islamic legend also claims that King Solomon had his own flying carpet, and this page claims that they also featured in Egyptian, Tibetan, and Indian legends. So I'm not sure of the original source of such rugs, but they were surely the greatest invention since pita bread.
Oh, and by the way, happy birthday to gloworm59!