The herd immunity was basically what the US and especially UK were doing until the leaders of those 2 countries were shown modeling of what that meant in terms of mortality. in the US is was anywhere from 1.2 to 1.7 million deaths (in a country with 350M people even a mortality rate of just 0.4% is over 1M if not one has immunity). in the UK, 250K. Not an elected politician on the Earth is going to be willing to just go along with that.
This is a virus that was originally an animal virus for who knows how long, in Nov 2019 it spread from an animal to a human for the first time. Within a couple of weeks it mutated to where it could spread person to person. And according to something I read today it has already mutated again so there are 2 distinct strains. It's been an incredibly hardy and aggressive virus that has shown the ability to mutate and replicate easily. Since it is something that came from the animal world and is not some sort of previous flu type virus there is no immunity for humans right now. There also have been cases overseas of re-infection (though it is just as likely that it was never fully recovered from).
The other problem with the herd immunity process is that you overwhelm your entire healthcare system so not only do you have deaths from the virus, but your mortality rate for others that come in with heart attacks, cancer, broken bones and other ER issues go up as there is not space or resurces for them.
The 1918 H1N1 Pandemic is a good one to study. In the US, areas that chose not to cancel public functions and pretty much went on living how they were living (in particular Philadelphia and Baltimore) ended up being the most hard hit areas in the US. it also caused secondary outbreaks as people went back to normal and it spiked again - Boston. Obviously anywhere with really high population is going to be more susceptible to a breakout. Hence the numbers multiplying very rapidly in NYC and surrounding comminuties.
I'm not a big fan of deficit spending but right now is actually the appropriate time to be doing it. The government is going to have to support both business and workers (the first part is going to be very politically unpopular and seen as government handouts to businesses and the wealthy). My belief is they will likely have to do more than 2 payments to individuals and the payments may have to be higher as this drags on and more people are released from jobs as payroll tax cuts only help those who have jobs. But there are certainly industries that will go under without government help as well. I'd make the assistance to companies work similar to TARP during the Financial crisis. Basically a loan that will have to be repaid at some future time that is not completely specified. The Federal government ended up getting all its money back plus interest from TARP.
There was also a very good article yesterday on CNN by a doctor that looked at differences between SK and italy in terms of infection population. It went far beyond testing (though that was a big help for SK in identifying people early and getting them quarantined). But in general, Italy had an infected population that was older, more male and more smoking and underlying disease issues. in South Korea the infected population was younger, more female and less underlying medical complications. The mortality rate is almost twice as high in men than women and those who smoke or have underlying conditions vs those who don't.
Herd immunity would have the pandemic run its course much more quickly, but at a cost that most people would likely consider unacceptable.