I'm not sure what there is to misunderstand. Heat is taken for the outgoing hot air, and transferred to the fresh air coming in. So instead of hot air going out, the air going out will usually be freezing.

In my experience, people usually try to avoid exchanging air with the outdoors when they're concerned about significantly heating/cooling their homes. If you're exchanging air then a heat pump could super heat/cool the outgoing air, and that's the piece I was missing from your proposal.

A house must exchange air. Better insulated houses are basically air tight, so you must have ventilation to get fresh air.

A pro with that solution is that the extracted air has a high temperature all year, making it more efficient that using a heat pump to extract heat from outside that might be -30 celcius. A downside is that the amount of air is limited, so if you need more heat then you have to supplement it with something else.

You get it, but it seems there are a few others that don't realize that a heat pump can also be used to increase efficiency by reducing the heat lost. While I do get that it's unknown to most people, some people here perfectly illustrates the Dunning-Kruger effect...

That sounds like heat recovery ventilation; while useful, it serves a different purpose than heat pumps (which heats up enclosed spaces without the ventilation). Also HRVs normally work with whatever existing air and don't use extra heated air…

You are recovering the heat from the ventilation, yes. But you're doing so using a heat pump.

Check out e.g. Nibe F750 with SAM40.

I'm using the heat pump to heat water using the extracted air. That water is then used for floor heating, ventilation air heating and ofc. hot water.