I don't believe Levitt's interpretation. I certainly hope it's true, but I don't think it is. He seems to believe containment measures have no effect, which is implausible to me.
He's just talking about the stats, without giving a biological hypothesis for why infections would top out - that seems to be coming in an upcoming video that hasn't been released yet.
I'm also a bit sceptical about his conclusions. The effects of containment measures aren't really visible in the curve, but e.g. Sweden has a much worse exponent - increasing the chance for more outbreaks will also change the parameters for Levitts curves. I think Germanys curve got very slightly worse recently (shops opening - masks didn't compensate). But I'm not sure if masks did anything at all - there is no clear trend-break in the growth-rate of Germany. Also masks may just keep a local population infectious for a longer time - increasing the risk for visitors.
One biological hypothesis is that covid-19 spreads in local clusters - and has a hard time to move to other places. (e.g. it might need 20 minutes of close-contact talking) The growth-rate is shrinking exponentially (something that Levitt noticed, and can be seen everywhere)- each outbreak locally is trapped and doomed to fizzle, because it is competing with itself - it's just not mobile enough to move to another location before it burns out to maintain a constant R=1.
France has already lifted many of their lockdown restrictions.
> Assuming we'll all contract COVID-19 anyway, eventually,
That's a big assumption, and not necessarily correct.
First, we won't all get it - herd immunity means infection rates max out at something like 60% to 90% of the population. I understand this maximum is to some extent a function of how fast your infection rates rise due to a sort of momentum effect.
Second, we may be able to suppress maximum infections indefinitely (or until we get a vaccine or treatment) with tracing, local lockdowns and so on. It's not clear if this is an effective long-term strategy, and is disputed by some epidemiologists, but seems to be the leading preferred strategy by most experts.
> it makes little sense to adopt strong restrictive measures on personal liberty to slow the spread down to a crawl
The problem is that you can't really adopt half measures. That's linear thinking, and it's an exponential curve. You either keep the reproduction rate above 1 or below 1. Above 1 you get an accelerating increase and eventually overwhelmed hospitals. Below 1 your infection rates start halving.
Luckily, the measures required for keeping R<1 don't seem to be too intolerable. Spain, Italy, France etc. have managed to squash their epidemics and are getting close to having something like normal society back.