I see a couple problems with this.
First, you have to install a return pipe from the shower valve to the fresh water tank. This is easy to do while the RV is being built, but once the walls and the floor are closed in, it is very hard to do.
Second, the re-circulation idea works well as long as you are using water from your fresh water tank. But when you hook up to city water, you have to remember to turn off the re-circulation function, or it will fill, and then overfill, your fresh water tank.
Finally, the splashy overblown ads really annoy me. They start off talking about saving "gallons" of water. Actually, there is maybe 6 feet of half-inch pipe running from the water heater to the shower, and the amount of water being saved is the amount that is in this pipe when you start your shower. While I have not measured it (any volunteers?), the amount of water in this pipe calculates out to about a cup. There are 16 cups in a gallon, so you have to ask yourself how much work and expense you are willing to do in order to save one cup. If you are boondocking in extreme dry conditions, maybe it is worth it - though in extreme conditions you likely won't be taking many showers.
In my opinion, a much better idea is to get a shower head with a shut-off button and maybe a variable flow rate. With these, you can take a Navy shower using well under a gallon of water. Check out post #8 here
https://www.trailmanorowners.com/for...ead.php?t=2331
Bill