the climbing rate gauge should have HUGE variations caused by atmosphere

Actually, pressure can change a lot at a particular level, that's why Altimeters are adjustable (barometric setting knob). This setting is most easily found when on the ground, just turn the knob till you have set the airfield elevation on the instrument. In flight, corrections must (practically) be sent by radio from weather or control centers and be relevant for the aircraft's location. Corrections are then, obviously, periodically needed during changing weather conditions. None of this really has any bearing on the vertical speed instrument, as it reacts to level altitude pressure changes (as while sitting on an airfield) much too quickly to register any vertical speed errors. Sit in a parked aircraft while a storm blows through and you won't see the VSI move at all.