Indoor Air Quality
I have 7.5 years of environmental services quality control management in large hospital settings. I've helped get manufacturing clean rooms in compliance with particulate problems. I've written cleaning procedures for surgical room "sterile zone" areas.
Here is the good news: Carpets are wonderful heavy particulate (dust) filters. Vacuuming every day will reduce the heavy particulate count in your home. HEPA filters improve removal of smaller particulates - especially dust mite / pet hair triggers. The number one source for dust is a human - shedding over 500,000 skin cells per hour just sitting, and 10 times that moving around. Vacuuming won't improve exposure to volitile chemicals, or radon.
So, vacuuming improves indoor air quality. HEPA filters take out fine particles. If you want to keep a room relatively low in dust - don't use it. You are the source for at least 70% of the dust.
Vacuums do nothng for removing VOC's (Volatile Organic Chemicals), and radon. HEPA filters can capture mold and bacteria. Filtering mold and bacteria does not address the source, though. Wiping down hard surfaces with sanitizers, and keeping humidity down is what keeps those issues in check.