I've tried to make the idea work in my head many times but my conclusion has been that I don't think there's quite enough co-incident demand for heating and cooling in the average house. For example, yes, I could generate all my domestic hot water from heat from air conditioning in summer, but in winter I need to be able to generate it plus heat the house, so I need enough capacity to generate that heat from the outside air when I'm not using air conditioning (so I don't save on not needing as much capacity), and the efficiency gains probably aren't worth the extra complexity.
For applications like commercial buildings, public swimming pools, industrial sites, etc. can (and increasingly do) definitely benefit from that kind of combination though.
For applications like commercial buildings, public swimming pools, industrial sites, etc. can (and increasingly do) definitely benefit from that kind of combination though.