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.