I didn't know that was a thing! I've been thinking of that exact same thing for years, wondering if it was even technically feasible and wondering why it wasn't a standard in new home construction. I can't imagine how much water is wasted by people just waiting for their showers to heat up.
Then again, my local water company recycles waste water from people's homes. So maybe requiring it isn't necessary with modern water recycling programs.
Is it weird with your cold water? Looking into it, it seems like it fills up your come water pipe with warm water. Wondering if that affects drinking water coming from your refrigerator or anything like that.