Carpets act like the filter in a fish tank. They trap allergens between fibers and prevent them from circulating throughout a house.
Carpets also reach a critical mass, and then walking on them disperses particulates throughout the environment. There's a reason old carpet usually weighs more than what it did when it was new.
Meanwhile, hardwood or tile floors definitely refrain from collecting particulates, but they also don't act in the same capacity a carpet would as filter.
However, it's easier to tell when a hard floor needs cleaning.
Earth-friendly cleaning tips
The best way to keep dust from accumulating over time is to regularly clean the floor. Daily is best, weekly more realistic, and a monthly cleaning can be as effective, but won't be as effective as more frequent cleanings. When cleaning regularly, hard areas are hit multiple times over several cleaning cycles; eventually only a modicum of mess remains.
Shoes don't just pick up dirt and bits of mud; they'll also get pesticides and lead on them. One of the best cleaning tips is to ensure shoes are removed and left on doormats at entrances and exits. Also, shoes should remain by doorways, not be worn in the house. This will keep most avoidable problems at said doorways. If there is a strategic doormat beneath, then beyond sweeping or vacuuming, the only floor cleaning work you've got to do is to beat that thing out once in awhile.
Damp Mopping for Wood
Wood soaks up water and will warp if there are regularly puddles on it. You don't want your mop soaked and leaving trails of water. It must be damp. This is an easier, green way of cleaning the floor without getting on hands and knees.
There are no shortage of toxic solutions out there for cleaning the floor. If you want your floors clean enough kids can crawl on them, getting a doormat somewhere strategic to keep the lead and pesticides out is a great step; but cleaning with some miracle solution is likely to leave as many toxins on the floor. The best non-toxic solution for cleaning is about a quarter cup of liquid dishwashing soap and a bucket of warm water. Scuff marks can be reduced with a damp sponge and a little baking soda.