Mixing folklore textures, manga craft, and fan fever, the origins of the tengen wives legend really feel like a braided rope of sources rather than a single spark. In-universe, the simplest root is in 'Demon Slayer' itself: Tengen Uzui is written as a flamboyant, ex-shinobi Hashira who works with three women — Suma, Makio, and Hinatsuru — and the manga/anime frames them as his wives and comrades. That choice by the creator planted a vivid image that was unusually cinematic, because the scenes in the 'Entertainment District' arc highlight theatricality, family ties from a ninja background, and an almost kabuki-like performance aesthetic. Those story beats give readers a plausible, diegetic reason for why he would have three partners: they were trained fighters, partners in raids, and part of his personal code of protection and showmanship.
Outside the story, historical and cultural threads feed the legend. Polygamous relations and concubinage existed in certain periods of Japan, while kabuki and traditional theater often celebrated flamboyant male performers and stylized romance, which resonates with Tengen's look and manner. Fans then took the canon seed and ran: shipping, fanart, memes, cosplay groups, and lore-building turned the simple line in the manga into a full-blown 'legend' online. So the origin is simultaneously textual (what Gotouge wrote), cultural (theater, shinobi tropes, historical practices), and communal (fans amplifying and mythologizing). Personally, I love how all three elements mix—it's part kawaii, part tragic ninja drama, and part internet camp, which makes the whole thing impossible to resist for fans like me.