Apples and bananas definitely should not be kept in an enclosed space as the gases will cause faster ripening. When apples are stored professionally they are stored in a nitrogen environment with CO2 scrubbers which can make them last for months. Bananas typically come in plastic bags unripened so that they last longer on store shelves. Tubers can generally last a very long time in a dry cool place, which the fridge is not. It's why people used to have root cellars.