Tiles, floorboards etc. do not hold on to dust, rather it gathers up in corners. When the front and back doors are open, the wind comes through blowing the dust up into the air (this is what you can see when the sun shines in) and this is now what you are breathing in. In the case of a well-maintained carpet, the dust is held in place between the pile until it is vacuumed with your upright vacuum and disposed of outside with the rubbish.
Dust mites live wherever humans live. They only cause problems when their numbers are allowed to build up, but regular cleaning and maintenance will prevent this. Often, when there is a problem, the carpet gets the blame, but don't forget to make sure that the bedding (pillows, blankets and mattress) is also regularly cleaned, vacuumed and aired! After all, we spend a third of our lives in bed, and this is where the dust mites really thrive!