We may not have a choice, in that we're not guaranteed to have a useful vaccine in massive doses anytime soon.
But rebutting your individual points:
> millions would die
Unlikely. Improved estimates (thanks to serological data) for infection fatality rate range from 0.3% to 0.5%. If we can protect the most vulnerable populations, we can have a lower death rate than this-- e.g. in the under-30 crowd, the risk of hospitalization is 1 in 500 and the risk of death a tiny fraction of this (1 in 5000 or less).
Further, any variance of susceptibility or contact density means you don't need to reach 60% for herd immunity. Some estimates say that the real threshold may likely be 25% or less: e.g. https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v... Further, lighter weight social distancing measures can further reduce Rt and attain herd immunity at a lower percentage.
If you assume we need 40%, and 0.25% IFR from protecting the most vulnerable-- you come up with 328k deaths. This is bad, but less bad than many alternatives. Note that the shorter lived the controls protecting the elderly and other vulnerable people, the more effectively we can protect them, too.
> health systems would get crushed
We'd not want to do what New York did, but let's look at it as an example. New York's health care system (barely) sustained the load. Now they're very possibly most of the way to herd immunity in NYC. Yes, we'd like to flatten the curve a bit from this and be better prepared.
> the virus is unlikely to disappear entirely, so would simmer around the world, triggering epidemics every few years or so.
The long term immunity question is interesting. Of course, vaccines could help improve this picture even if one ends up with disease-spread based herd immunity.
My personal belief is that A) total antibody-based immunity will last a few years, based on our experience with SARS-CoV-1; B) partial antibody-based immunity will likely last longer than that; C) memory B cell / T cell based immunity is likely lifelong and makes any subsequent course of disease less severe.
That is, I think it's likely that the current human coronaviruses that cause the common cold might very well cause a high death rate and be very transmissable if exposed to an immunologically naive population.
Of course, your third point holds even more true when it comes to interim suppression and containment efforts while we isolate and wait for a vaccine. It's an even more intractable issue to try and maintain suppression when the vast majority of the population is still susceptible.