Typically on the little fridges the freezer compartment acts like a radiator if you will to cool the fridge. That is why they ice up so much when the doors are opened and closed. So I think this is why people have problems with things freezing up or nonuniform cooling when they are modified by bending down the freezer. They no longer have the air moving across them as well as there isn't a fan or anything circulating the air like in a larger kitchen style refrigerator. I would think if a small fan were installed in these fridges that it would help with uniform cooling and the operation of the fridge. As for cutting out the freezer, I don't think that would work so well. It would be a lot of work and you would most likely break the circuit of the "radiator" that is the freezer. This would allow the refrigerant to escape and you would have little more than an igloo cooler.