The whole notion that somehow we can achieve natural herd immunity and then our problems are solved strikes me as flawed at a lot of levels -- the more I think about it, the more levels.
1) Empirically, it generally hasn't worked before, at least with viral diseases. We never achieved herd immunity for smallpox, measles, polio, chickenpox, etc. without vaccines. There were always periodic epidemics of these diseases after the initial outbreak -- whenever it was -- went away. With smallpox, we have the example of it being introduced into North America deliberately as a biological weapon. It had tremendous mortality at first. It was less lethal after the initial outbreak, but it didn't go away and still killed a lot of people until vaccination became universal.
Polio might be one of the best analogues for this. It has been around for a long time, it tends to cause less serious illness in children, and only a small fraction of those who get it have serious effects (on average 0.5%), with only 30% showing any symptoms (both of which are lower than with COVID-19). Oh, and then there's post-polio syndrome. Yet the population as a whole never developed immunity until vaccines came along. There were periodic outbreaks, and the response was basically what it is now -- close everything down during the outbreak. The mode of transmission is different for polio than for COVID-19, but the level of contagion was reasonably similar, and while individuals acquired immunity, there were still enough susceptible people around so that outbreaks were able to take hold.
Measles is far more contagious than COVID-19, but not everyone got it in early childhood; many got it later in childhood. So we're certainly not going to reach an immunity wall very quickly (and probably not at all).
We're still in a much earlier stage of COVID-19, where most of the population is susceptible and outbreaks can spread very easily if we're not careful. Yes, life went on with diseases previously, but there was a greater degree of resistance, and as a result of these diseases a lot of people led shorter — and sicker — lives.
For that matter, we don’t even really know what “immunity” means. How long does it last? Does it reduce the chance of a serious case the second time around? We’ve seen a few people apparently get sick a second time, and in at least one case the second illness was worse than the first, but we don’t know whether people might get infected asymptomatically and spread it without ever knowig, because we don’t routinely PCR test people who have had the disease.
2) "Herd immunity" is really a misnomer. "Herd resistance" would be a better description. It's not "the population is susceptible" or "the population is immune". We're not going to reach 70% or so infection and then magically it's going to go away. With no precautions, that might get the R overall below 1, so it won't spread as easily, but some places will be touched less than others in the current early stage, and there will be chance accumulations of people who aren't immune (perhaps, as I noted above, because immunity might not be lifetime -- it generally isn't with coronaviruses), so there will be outbreaks. With R only a little below 1, it's going to simmer along, but the R will decrease more slowly as there are fewer people susceptible, and as new people are being born there will be a steady pool of susceptible people, it's going to reach steady state. Which means continued outbreaks. And since not all adults will catch it early, there will continue to be people at risk getting sick.
The only way we really stop disease in its tracks -- get R so low that the few people who have it have very little chance of spreading it at all -- is with vaccination. As we've seen with measles, when there are clusters of unvaccinated people, it takes hold.
3) The idea that we can somehow protect the people at high risk is a fantasy. How are we going to protect nursing homes? Test everyone -- particularly staff -- daily? Make nursing homes bubbles, where the staff have to live there under bubble conditions? How many people would work in assisted living if they're expected to quarantine more or less forever? If you think lockdowns for a few months are bad, think about what that means if people are forced to lock down for years. There will still be false negatives, so it will have a chance to enter. The NBA, WNBA, and NHL successfully implemented bubbles, but those were small numbers of people, and there's enough money in pro sports to actually do it right (and we’re seeing that MLB and the NFL can't). But that won't work for senior living facilities.
Essentially, it's saying "let's imprison everyone living and working in an assisted living facility so that I can go out and have fun at a bar". That's not some principled notion of freedom. That's simply selfishness dressed up in fancy rhetoric.
The goal of public health measures now is to keep as many people as possible safe to buy time for better detection, treatment, and ultimately a vaccine or vaccines. It's a bit different than with polio for much of the 20th century, where the goal was simply to break the chain of transmission until it went underground after the summer. Here the hope is that we'll be able to actually do something about it, and keep people healthy pending that.