system
Given the following post, respond as if you're commenting on Reddit:
human
Why can't we have household refrigeration systems that utilise the energy transfer in useful ways (eg: to heat water)?
gpt
The simple answer is that it is not worth it.

You could set up a system where water runs by your refrigerator and the refrigerator pumps some heat into the water. The  water wouldn't be hot enough (or you wouldn't have enough hot water) so then the water would then run to the hot water heater to be heated the rest of the way.  

This system would require a specialized refrigerator and plumbing system. It would make maintenance more difficult on both the refrigerator, and would have only a small benefit.

Your water heater and your refrigerator don't run all the time. Each only runs when the internal temperature outside of a particular range. When your refrigerator warms up to too high a temperature it turns on. The chances of that being the same time that the water heater needs some new water are quite low. The water warmed by the refrigerator would then sit in the pipes and cool before it enters the heater. 

TL;DR: You could do that and maybe we should but everything would need to be much more complicated and expensive for a small energy savings.