Like I said, "simple infection model (the SIR model)".

Which more rigorous models have the area under the curve as roughly the same, as you describe it?

I believe any model which has herd immunity, where personal immunity comes after a period of infection, must have the possibility of overshooting the minimum heard immunity density when the infection rate is high enough. As in the SIR model.

Lower the infection rate and there's lower overshoot.

My point is that that the argument you made - i.e. that lower transmissibility aka. "flatten the curve" lowers total mortality in the SIR model - doesn't hold unless you assume that you can keep transmissibility down forever (and unless a vaccine or treatment comes out fast enough). That is, I'm not presenting a new argument, merely refuting your argument, over the SIR model you used, adding the assumption that transmissibility can't be kept down indefinitely - which I believe is very reasonable given what we are observing.

I believe it's the burden of the proof is on you to present a new, more rigorous model if you want to argue that slowing down transmission significantly lowers overall mortality - as the null hypothesis is that they are not associated.

On the last point, I am aware that under the SIR model, there's the possibility of overshoot, i.e. exceeding the minimum herd immunity threshold. My understanding is that this isn't a significant effect unless you have uncontrolled, explosive expansion, so that most people get infected simultaneously before others develop immunity and can therefore act as a barrier for herd immunity. I don't believe this is the situation right now given the numbers we are seeing.

That said, I believe that the more realistic future is that a vaccine or an effective treatment will be developed in the next months, and that will be the thing that will have made temporarily lowering transmissibility worth it. What I don't believe, because I haven't found any evidence for it that holds basic scrutiny, is that if no vaccine or effective treatment can be developed in a reasonable timeframe, then keeping the measures to slow down transmission as long as possible will have any significant effect on lower overall mortality.

EDIT: To make it clear so people do not misunderstand me, what I believe has no evidence is that without a timely vaccine or effective treatment, slowing down transmission beyond what is necessary to keep the health system from overloading is associated with lower overall mortality.

The argument I make is that jb775's assertion at https://news.ycombinator.com/item?id=24586075 ("People seem to forget that the expected total death count from day 1 was, and still is, expected to be the same no matter what actions taken") is wrong.

I say it's wrong because months ago I heard arguments that models predicted that lowering the curve could also reduce total mortality. And I linked to that video to give evidence that this was part of the general discussion months ago.

The fact that you disagree with that model, or argue that I need to give a stronger evidence for the current information we have, has no bearing on my point.

Eg, when you write "I don't believe this is the situation right now" - that statement is based on knowledge you have now, not knowledge that people had on "day 1".

Fair enough, I understand your point better now. I also remember hearing a lot of arguments for lowering the curve lowering overall deaths back in March - either by heavily suppression or elimination of spread, or by a vaccine or effective treatment.

Nowadays it seems both EU & US hasn't pursued heavy suppression (probably too costly, and legally and culturally difficult), but rather just hoping to keep it somewhat under control until a vaccine comes, hopefully.