I expected this idea to be more baked than it turns out to be. Looks like the reason for that is mainly that it's just economically half-baked. I've seen a patent that appears to claim the idea, but I'm pretty sure just a little more digging would reveal prior art.
We already have split unit air
conditioners that are less inconvenient to install than the "wall bangers" of old; so why not do the same thing for fridges?
I suppose before even asking why not, one first needs to ask why. Why? Well flexibility, in a nutshell (and to a lesser extent, not making the fridge fight against itself.)
If your coolth supply came in through the wall in some kind of pipe (maybe), you could duct that (suitably lagged) to wherever was convenient. The circuit could branch through your milk and butter cupboard (you do hate hard butter, right?) and be controlled in there to give you say 11 deg C. (You do hate runny butter, right?)
It could go up into the ceiling to your long-term freezer where you keep the bodies of your victims at a steady -17, pending processing.
Finally, it could even visit your beautiful mahogany refrigeration closet, where you keep all the beers.
You get the picture.
For a "piped fluid" system, you could use water, a lot of anti-freeze, and the lowest temperatures possible.
It would be a lot less noisy than your fridge is going to get when it gets old.
For people in hot countries this makes sense purely from the point of view of not heating the air around the fridge, thereby heating the fridge, thereby forcing the heat pump to do more work to offset this.