In fairness, you reference a single retailer. And that's really important here - retailers will always have a significant markup. You want to go to a wholesaler like CE [1] for a good deal. Most HVAC wholesalers and suppliers will give walk-ins an above wholesale price, which is still less than retail.
Most people are not able to install a heat pump themselves. I consider myself a fairly technical DIY sort of person but was not comfortable installing it myself. Installation is going to be the majority of the cost for the typical person buying a new heat pump.
The labor to install mine was $450. Granted I'm in the Southeast of the U.S. so YMMV, but that is not universally true and shouldn't be stated as such.