I'm looking at going this route before I finish the basement. The master shower is the furthest point from the heater, and it takes a solid 2-3 gallons to get hot water in the morning. The math didn't make sense until I put in a heat-pump water heater. Now I average $170/year to heat my water, and the recirc should only add ~$30/year. My pipes are well insulated, but I'm in a colder climate so loosing heat into the walls just lowers my heating bill.

I installed a recirculating pump and had it on the timer. But then for some reason, I switched it to always on and it's so much nicer. Hot water is always hot.

I’ve been tempted to do that. Sometimes I wake up at odd hours when it’s not running.

I wash my hands with the cool water that initially comes out?

Cool water? What about freezing water in the winter?

I am still waiting for the freezing water to come out of the tap.

Assuming your pipes are between the tap and the water heater, and the pipes run indoors, the water temperature will be close to room temperature - nowhere near freezing.

Which was a problem in NL because the bathroom of the airbnb was not well insulated. And there wasn't a hot water option because... NL.