Heat pump Not turning off

The reason furnaces (as opposed to heat pumps) keep running is to cool them back off since the burner is pretty hot. It may be a safety issue (too much undistributed heat could make the furnace hot to the touch and possibly result in a fire), but I suspect it's also done to extend the life of the furnace from large temperature swings with the side benefit of a bit of extra heat distributed through the home rather than up the flue.

From a heat pump, I suspect the temperature inside the blower is below the setting used by a high temperature switch in a furnace (which is what keeps the blower running). Also, circulating the coolant in the lines is what causes the heat to be generated, so if you were to do this, at what point would you stop?

And finally, the heat that is in the vents will naturally rise, so turning off the blower will not result in that heat being lost. If your vents are in the ceiling, the rising hot air will go back into the vent over time even if you blew it out. And if your vents are in the floor, the heat will rise as colder air displaces it, without having to run the blower.

So can you get a little more heat out of the system? Perhaps. But I believe it will be very little. And since drafts in the home make you feel cooler in the winter, the result of saving that extra heat may result in you feeling the need to turn the thermostat up a bit more.

I've been told that a properly sized heat pump should run almost non-stop during the days that the temperatures are the normal low for the season and area. Any lower than the normal seasonal lows would kick the strips on.