You are correct. Remove the carpet (the filter) and you (the homeowner) become the filter.I had a client that told me because of her allergies she was going to rip all her carpet out and replace it with hard wood flooring...I explained to her the above but she went ahead and did it anyway...a year and a half later she calls me to come and do a warranty clean on her new carpet....she found out she was twice as sick when she put in the hard wood....
I can see the value of emptying the sink (the carpet) but air? A HEPA air scrubber will drop the allergen level in a few hours as it processes the air and captures those allergens larger than .3 microns.
The humidity would probably increase the suffering for those allergic to mold spores. We use particle counters to measure particulate in the air. Just walking through the room will elevate the counts. Vacuum with a non HEPA vacuum and those counts go through the roof. We live in a highly humid area so I'm not sure what dry climates are like.How bad is the dust level in a home in the areas where there is high humidity..compared to ares that are dry and have hardly any.............do dust partials dance around in thick moist air........??????
I have lived in humid areas and cant say I have ever paid any attention to this................