I think there is some concern of intranasally applied substances getting into the brain.

Even plain water infested with certain amoebas can give you a fatal brain disease if you use it for nasal irrigation. It is perfectly safe for drinking, though.

https://www.healthywa.wa.gov.au/Articles/N_R/Nasal-irrigatio...

We do not have that amoeba here, but I still boil the water and cool it down before using it to flush my nose. (Works great against mild common colds.) One of the worst outbreaks in the world actually happened in Czechoslovakia 60 years ago - 16 people died after being infected in a public swimming pool.

There's an approved nasal vaccine in the United States (FluMist). It's use was not encouraged for a while because it didn't vaccinate against H1N1 (recent years have included H1N1). It doesn't look to be particularly more effective than the shot (marketing focuses on no shot, not on it working better; the CDC says the effectiveness is similar).

There's multiple candidate intranasal SARS-CoV-2 vaccines, just none that have concluded trials.

Oh, yeah, I received a nasal vaccine against flu in the early 1990s in Czechoslovakia as well. It wasn't a match for the coming wave, unfortunately, and we all got very nasty flu.

They are being pursued, just not given the same resources as the emergency effort to get the original vaccines approved:

- https://www.biorxiv.org/content/10.1101/2022.01.24.477597v1

- https://www.science.org/doi/10.1126/science.abg9857