> there are plenty of cases where we have had essentially purely phenomenological models in physics
Actually, there is a fairly common point of view (which often goes by the name of "effective field theory") according to which all of our physical theories, even the ones we usually refer to as "fundamental" like General Relativity and the Standard Model of particle physics, are phenomenological; they aren't the actual "bottom layer" but something that emerges as an effective theory from other layers deeper down (which we don't have a good theory of at this point).
Actually, there is a fairly common point of view (which often goes by the name of "effective field theory") according to which all of our physical theories, even the ones we usually refer to as "fundamental" like General Relativity and the Standard Model of particle physics, are phenomenological; they aren't the actual "bottom layer" but something that emerges as an effective theory from other layers deeper down (which we don't have a good theory of at this point).