A: Moving Heat and Cool air.
Q: Air moves in what motion or direction in a room?
A: It circulates. (moves in a circle)
These answers address the problem I have had with whole house units - because the air "circulates" the strength of air movement into a room from the vents is insufficient for proper cleaning. The vent air doesn't push and the recirculating vents don't pull air back at a strong enough rate (CFM) to clean the air. The vents also tend to push/pull it in a "non-circular" path. So for those with allergies and asthma you're not going to get a true changeover of air 3-4 times an hour as I (and Doctors) recommend.
The only exception I have seen is if the house is custom-designed or built specifically for air purification with separate "zone-base" fans. If you're counting on a single whole house fan or blower motor it will be energy inefficient if it's on all the time. And if the heat or a/c is off (with the blower off) then of course you're not cleaning the air at that time either.
However I will say that the filters on the heating or cooling system are important - to collect dust and soot from the furnace before air goes back into the room. I'm just saying that the whole house approach to cleaning isn't the best approach from a financial as well as an effectiveness standpoint
The air purifier I had was on all the time, unlike the air conditioner, and used less electricity than running the whole house fan all day.
Note: I use an air cleaner in the rooms I use - just my office, living room, and bedroom - the rooms I spend the most time in.
I started using these when I was young and had bad asthma and allergies, and it helped.