[samatman]

They mechanically open the nostril, which resists sinus closure, and that has knock-on effects for the rest of the respiratory tract. Nostrils basically don't block unless you stick something in them, but sinuses do, and opening the nostril helps directly with that. As a sinus starts to fill or close, it gets harder to pull air through the nostril, and noses are pretty flexible, so the passage narrows, which further narrows the sinus. Eventually you have a blockage, and start mouth breathing, and that's what triggers the blockage you're referring to. Sinuses serve an important purpose in humidifying air, which is important for the proper function of tonsils, especially the adenoid: adenoidal swelling is the major cause of apnea, and dry air from mouth breathing can easily trigger it.

It doesn't work for everyone, and some people are just going to need a CPAP. But it's a no-commitment intervention of negligent cost, and if it works, that's a much better outcome than needing a CPAP and everything which comes with it.

But there are actual, demonstrable reasons why it can serve as an alternative to the CPAP for some number of people, it isn't just woo. I hope I've done a good job of explaining why that is.