instant hot water (primary bedroom is across the house from the water heater, so without that recirculation it can take well over a minute to get hot water).

The pump is on a timer and runs several hours each day. With a hot water tank, the heater doesn’t really even come on at all when the pump is running- the slightly less hot water is just returned to the insulated tank.

For a tankless, it would have to fire up to run the pump, and I don’t know what happens to the water coming back from the recirculation. Does it go back through the heater?