The traditional North American split system heat pump (ignoring "dual fuel" systems for now) relies on a backup heat source to provide both makeup heat during low-temperature (below the system balance point) operation and, more importantly for this, outdoor unit defrost cycles. This backup heat is typically supplied by heat strips, and generously sized ones at that, considering that during defrost, the backup heat must carry the entire house heating load.
However, as documented in this Mitsubishi application note and this government research paper, mini-split heat pumps stop or radically slow their indoor fan when defrosting to avoid filling the room with cold air, since they do not have a backup heat source to run during defrost cycles. This has the downside that they are not actively heating during defrost, but even without that, they are able to provide heating in most climactic conditions using this defrost strategy and sensor-based defrost cycle triggering without aid from a standby heat source.
Is there a reason that one could not use a couple extra wires in the outdoor unit cable and an inexpensive fan relay to retrofit a split system heat pump with the ability to perform a "fan stop" defrost cycle instead of turning the standby (backup, emergency) heat on? This seems like an obvious target for energy savings, given that emergency heat is far more power-hungry than heat-pump heat. Furthermore, even without any energy-efficiency benefits, this would likely allow the backup heat to be significantly downsized in climates where it's not heavily relied upon, as now it only has to be sized to make up the heat pump's capacity deficit at the heating design (99%) outdoor air temperature, not the entire house heating load. This can reduce electrical service sizes, and also position the system to be more easily handled by a backup generator.
Best Answer
During the defrost cycle, inside heat is not being pushed to the outside as you stated "the parasite heat load of heat that is being pushed from inside to outside to defrost the coils themselves". The inside fan has to run to insure that the liquid refrigerant entering the indoor coil is vaporized so that liquid refrigerant does not flow back to the compressor. The outdoor coil is defrosted by the "heat of compression". The temperature of the outdoor coil is elevated by the compressor pumping the refrigerant vapor to a very high pressure which produces a very hot gas to defrost the coil. Since the outdoor fan is turned off during the defrost cycle, the refrigerant does not condense and the coil pressure rises as does the coil temperature. The colder the outside temperature the need for defrost cycles is reduced due to less water vapor (humidity) being on the air. Less humidity results in less water vapor to coat the outdoor coil. The back-up heat is turned on to temper the now cold air that is being generated by the defrost cycle.-------- Add-on to answer; actually @ThreePhaseEel my explanation does answer your question; you asked if you could add a relay to shut off the indoor fan. You can , but do you want to gamble on slugging liquid into the compressor which may screw up the compressor. The indoor fan runs because it should. The heat strips turn on to keep the discharge air at a reasonable temperature. They do not have to run for the defrost to work.