Humans tend to not breathe in a lot of stratospheric aerosols, on account of that being pretty high up.

As they sink down, they grow larger (condensation & coagulation). Once they reach the troposphere, they usually get down via precipitation, which also isn't really affecting a lot of breathing.

They can absolutely have other effects (see SO2/acidification, e.g), but air quality isn't really the main concern. For SO2 specifically, there's actually very little mortality sensitivity: https://www.giss.nasa.gov/pubs/abs/wa01010x.html

You're right that the research isn't there yet to make statements with confidence, but that applies to the air quality claim as well.