The issue with herd immunity are the unknown long term risks. Just imagine this stuff wrecks your immune system a couple of months after infection. Or, that immunity goes away after some months.
There's no guarantee that herd immunity helps. On the other hand, we could be working all hands on deck to arrange our lifestyle AND protect from infection.
Flattening the curve was the most immediate and important goal, because overloaded hospitals kill a _lot_ of people.
Herd immunity by everyone getting infected should _not_ be a goal. That's still going to kill many, many people.
The estimate for the US by that route was around 2.5million dead. You could probably scale that by population size and maybe reduce a bit as we get better at treatment for this disease, but that's still a big number.
I don't think we have much option other than to prevent the spread as much as we can while waiting for something like a vaccine and/or far better treatments than we currently have.
Zero cases globally will indeed be a while, if it ever happens.
No one estimates a vaccine any time remotely soon and even with one it would take years at best to achieve zero cases globally.