What you are proposing is basically air conditioning, but for a small room (fridge).
I guess for a normal fridge splitting the heat pump into a dedicated hot side (outside the house) and cold side (inside the fridge) is just not worth the hassle, space and complexity.
For big fridges aka cold rooms they certainly use a split arrangement.
It would make sense in all kinds of climates, as long as the outside of the house is cooler than the inside.
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