There are a bunch of different recirculation systems. Some put the pump at the WH, some put it at the point of use, and how they work overall can end up the same. The pump requires power, and under a sink may or may not provide it easily, whereas it is often available near the WH. Some leave the pump running control the water flow with valves on each branch, some shut the pump off when the hot water level has arrived. None of the packaged residential systems get the water full hot at the point of use, so it isn't putting full hot into the cold-water return line. Mine shuts off at about 96-degrees, and a flush of the toilet clears nearly all of the warm water out of the cold line.