Yeah, the outdoor units are quite often not quiet. Which matters with houses on small plots very close to each other. For that reason a water-water (earth-water) heat pump would be preferable as that's much more quiet but also much more expensive.
My nose simply doesn't work with it, I get an allergy-like reaction that never stops (non-allergic rhinitis), and my wife has the same issue, and many people I know too.
Rhinitis is not exactly a disease. It's just a matter of your body getting used to it. Most likely it disturbs existing dust. Also - does your house have proper ventilation system? In high co2 environments I get rhinitis too.
Did you ask them? Not even billions, did you ask at least a few thousand? Nobody complained? I know for a fact many people working in buildings with forced AC complain loudly.
But if you actually did read what I wrote, there was no complaint from me about the cooling part of the AC.
What's wrong with heating air? It was the norm in every house I grew up in...