[reason-mr]

What you are referring to is a "screened bottom board" in langstroth (modern box) hive beekeeping terminology. Mites fall out of it when bees groom (if kept clean) and cannot return as they can only climb a certain distance (6" is what is generally held as being this distance). However, modern hives have other issues which may be more or less prevalent in different locations and some have argued they were primarily designed for honey production, not honeybee health. In my location, which gets quite cold in winter, the thin walls of langstroth hives have undesirable properties - being too thin to provide insulation, they get cold and then transpiration from the bees condenses as moisture on the inside of the hive, leading to mold. Other people see other problems - no hive design is perfect in all locations - many different location specific designs existed in antiquity, from the clay tubes of the Egyptians to the skeps of the English beekeeping and everything in between. I do note that in the wild, honeybees select a wide range of places in which to live, but seem (to many) to prefer hollow trees. Organization like boomtree bees and gaiabees encourage this preference by providing log type hives and report good results as well as evolved resistance to the varroa destructor, the parasitic mite to which you refer.