You're going to have to accept a ton of deaths to reach a 20% infection rate. Sweden hasn't managed to reach 10% yet by keeping society pretty wide open:
"Regardless of whether herd immunity is a goal or a side effect of the Swedish strategy, how has it worked out? Not so well, according to the agency’s own test results. The proportion of Swedes carrying antibodies is estimated to be under 10%, thus nowhere near herd immunity. And yet, the Swedish death rate is unnerving. Sweden has a death toll greater than the United States: 556 deaths per million inhabitants, compared with 425, as of July 20.
Sweden also has a death toll more than four and a half times greater than that of the other four Nordic countries combined — more than seven times greater per million inhabitants. For a number of weeks, Sweden has been among the top in the world when it comes to current reported deaths per capita. And despite this, the strategy in essence remains the same."
Sweden hoped herd immunity would curb COVID-19. Don't do what we did. It's not working.
If we can extrapolate to 1,000 per million deaths (roughly 556 * 2) to get to 20% infection in USA, that's 330,000 dead.
I think the bigger catch is that it all falls apart if we think it’s over and go back to 2019 behavior. If we do that, 20% is not enough.
If actual cases are 10X confirmed cases, AZ is already at 20%. (along with NY, NJ, Louisiana). That won’t help much if they throw the masks away and open it all up again. But it may decline the next few weeks if they keep the masks and distance rules.