Perhaps the solution is to rethink the role of the fridge in the kitchen. It could be designed to be a part of a kitchen island, or have cabinets placed above it. In conventional kitchens, a chest does not make sense. But it could be well integrated if we start with the assumptions the fridge will be a chest.

Refrigerated drawers in islands are definitely a thing in high end kitchens. But you typically have a large conventional fridge as well.