Having a heat exchanger let’s you exchange large quantities of outside air with indoor air at minimal costs. Trading 70f indoor air with -30f outside air is bad, moving heat between them means could be venting air closer to -10f and only need to heat the new air from 50f to 70f

You still want a quality filter and humidity is an issue in some areas, but overall they can make a huge difference.

Wouldn't a heat exchanger top out at equalizing the inward and outward bound air at 20F in this case?

The idea is "countercurrent exchange": the incoming air and outgoing air travel in opposite directions through the heat exchanger. The result is that most of the heat gets transferred.

At the end of the exchanger, the warmed incoming air is in contact with 70° outgoing air, so it will be at almost 70°. Similarly, the outgoing air will be at almost -10° as it exits.

It will probably make more sense if you look at the diagram: https://en.wikipedia.org/wiki/Countercurrent_exchange

Fun fact: "An example of countercurrent heat exchange occurs in the feet of penguins, in which heat from blood in the arteries supplying the feet is transferred to blood returning to the body's core in veins that lie close to these arteries."

No. Imagine that your heat exchanger is simply two touching pipes running parallel to each other, with flows in opposite directions. Incoming air will gradually warm up as it comes inwards, eventually being warmed by the air which has just left the room. You can get a much better result than just averaging the temperatures.

They are called air exchangers, basically the replace indoor air with outside air but pre-heat the outdoor air using a heat exchanger off the indoor air. So AQI definitely improves when they are run.

My house basically has a natural set point that the exchanger runs at per season. Much like my thermostat I can basically leave it at a setting for a season and it works well.

There are a few days I may have to slightly adjust things, usually when there's a big temp swing, so if it were more automated that'd be better but in general I have to maintain conditioned air in both the winter and summer to keep the house stable... and the house seems happier for it.

One can install HRVs and ERVs with no centralized system. We have, oh, three heat sources and half an AC in our house (old house) and can install a freestanding HRV or ERV simply as an air exchange (bringing in fresh air and letting out stale air). As we live in a cold climate, we're working out what we need in terms of HRV vs ERV. It seems like a slightly better solution than "leave the upstairs window cracked" which is what we do now.