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Not obvious this works though. 70% is herd immunity threshold when there is no epidemic. With an active epidemic it may be 95%.

Here are some epidemiologists arguing that: https://www.nytimes.com/2020/05/01/opinion/sunday/coronaviru...

538 made a model to play with: https://fivethirtyeight.com/features/without-a-vaccine-herd-...

So, the plan may be wrong. Proponents may have sincere but incorrect beliefs.

Note that in order for this kind of overshoot to happen, you basically have to have no social distancing whatsoever - not even voluntary changes to behaviour. If there is any then it decreases the reproductive number R further, meaning that it drops below one and the epidemic peaks before enough people have been infected to provide herd immunity after everything returns to normal, and then herd immunity is only reached during the overshoot past the peak.

(As I understand it, the UK government's original plans couldn't have lead to herd immunity in the first wave without this, since they were planning on substantial measures to reduce spread even under those plans.)

Basically herd immunity overshoot is a thing and shows up both in the historical data and in all models.

There is also the problem that as a virus takes years to burn through clusters of susceptible people. Currently it would take over a 100 years to achieve herd immunity in California.

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