Being in the mold business is really being in the air quality business.
If mold stayed on the wall or in the carpet, and did not contaminate the air, it would not be a concern.
Mold contaminates the air two ways, with spores (which are particles / seeds) and VOCs (Volatile Organic Compounds / fumes).
While it is always best to remove the mold conditions that are contaminating the air, certain situations may arise where you might have to 'manage' your air quality with a room air purifier. Also, many people who have allergies can benefit from the cleanest air possible. Actually, everyone can benefit from the cleanest air possible.
A good HEPA filter, along with a charcoal filter, can remove particles (dust, mold spores, pollen, dander) and VOCs (chemicals and fumes) from the air. Austin Air has 15 pounds of activated charcoal in the filter. The filters are basically a thickcylinder filter in a square box with holes that allow air to pass over the filters. Very simple and very effective. The filters can last 3 to 5 years so they are very economical. Just vacuum the outside of the box periodically.
The Austin has a high CFM rating (Cubic Feet per Minute) of air movement. That is also what makes them so effective...they move a lot of air. I see some air purifiers in homes and cannot feel any air moving...if it's not moving air, it can't clean air!
In my opinion, you should avoid any air purifier that releases ozone. This can include those that intentionally release ozone as well as those that inadvertently release ozone as a by-product such as air purifiers that use UV lights, electrostatic plates or ionizers. A good HEPA filter with charcoal helps clean your air, the other types can actually make your air worse as ozone can cause respiratory inflammation. Ozone should only be used as a de-odorizing treatment in unoccupied buildings.
I learned about Austin Air early in the mold business from a friend who is an industrial hygienist. He owned several and called them a 'work horse' of a machine. He was right; they work hard and last a long time.