Looks like someone trying to solve a non-problem. 1. Put your razor under the faucet, to eliminate the need for this contraption. 2. Don't use cartridges, and you won't need this contraption. 3. If you do use this contraption, it looks like it will make a mess on your counter.
It might be a little messy at times and one more shaving product to clean every once in a while. Like @DaltonGang mentioned rinse under the tap might be simpler. The concept is interesting and a oddity!
I soaked on the idea of getting a razor rinser, but I decided to wash my hands of it. For me, it was a sud-den revelation.
Own one already. Granted, it's a 100 year old design, but it does the same thing. Doesn't splash all over the countertop, either.
You fill the bottom part with alcohol. Put the razor in, and put the lid on. The handle sticks out through the lid. Rinse before using. Works fairly well, though alcohol evaporation is an issue, and it has to be topped off every week or two. It dispaces water and prevents rust or corrosion. 1920's-30's original. There's usually a few on eBay at any given time. That particular picture is just a random photo off the Internet, but mine looks almost exactly the same.