Quick proof that a Hammer and Dance (suppression) strategy is strictly better than Herd Immunity (mitigation):

1. Are you willing to collapse your healthcare system? If the answer is No, you need your transmission rate R equal or below 1 for the long term [1/5]

2. If you’re forced to have R below 1, you can do that starting with a baseline of a lot of cases (mitigation) or 0 (suppression).
[2/5]

3. Having an R below 1 while prevalence is high (mitigation) is awfully hard, kills a lot of people, and is worse for the economy since people are scared to catch the virus and don't go out to consume.
[3/5]

4. Having an R below 1 while prevalence is low (suppression) is much easier, kills fewer people, has a better result for the economy, and gives you more leeway to experiment what works best. All for the cost of a lockdown of 3-7 weeks if well managed.
[4/5]

Note that this requires good management.
But with bad mgmt, a mitigation strategy condemns a country to either keep bad restrictions for a long time (to be safely below R=1), or to go back and forth to lockdowns. There the pbm is not the strategy, it's the bad mgmt.
[5/5]