Problem with "herd immunity" is nobody knows if that is even possible. There are reports of people getting covid several months after initial recovery, they don't know if they are the exception or if everyone can keep getting it. Right now the repeat cases are less severe, but they are months later, what happens if you get it a year later? Is it still milder or will it be the same as the first time or worse? Even the vaccines are unknown, will people need them every 6 months, every year, or will they be good for life?
I don't think it is not possible to get covid totally under control with the way it works. If your infectious 3 days before you even know you have it how do you prevent that from spreading. You can lock everything down and mandate masks, but "essential" workers, which is about 50% of the workforce, will still be going to work every day. A certain percentage of the population will refuse to wear a mask no matter what. You're just not going to control it in a free society. We will probably just have to learn to live with it as we have with the common cold or the flu. And I am in no way saying Covid-19 is the same as the flu.