This device exists, you replace a vertical section of your sewer pipe with a copper heat exchanger pipe. The HX heats up your incoming cold water when you take a shower. The HX must be vertical because in a vertical sewer pipe, surface tension makes the water spread out and wet the entire inner surface of the pipe for good heat transfer.

I looked into the economics at one point. Would be great for a laundromat or hotel, not so much for the average single family home.