I don't think looking at it as a binary is the way to think about it. In other words, I do not think there is a Yes/No answer to the question: "Are lockdowns effective?"
For a while we were looking at Manaus and saying, "that's how you get to herd immunity," and then cases surged again there and, with no lockdown, their death toll was astronomical. Meanwhile, Italy, with strict lockdowns, has done only a bit better than the UK and worse than the US, despite having weather more conducive to outdoor life in March than much of the US and all of the UK and obesity rates significantly below the OECD average.
Even more to the point, Italy had much stricter lockdowns than Sweden and a much higher death rate (roughly 1700 per million vs 1300 per million). I conclude from those two facts that lockdowns CAUSE Covid deaths. Clearly.
But if we look at the situation in Italy with people dying untreated in hospitals hallways and bodies stacking up like cordwood, we can say that deaths definitely cause lockdowns. I have no doubt that if the situation in Sweden ever got as dire as it was in Italy at the peak, they would have locked down. As far as I know, however, Sweden just never seemed to run out of hospital capacity. Why? I don't think we know, but I will say for certain that it is not because they stayed open. There are other factors.
Back in the US, talking to friends and families who work in hospitals in hotspots, there were points in the pandemic when the medical system was being overwhelmed, nurses and physicians were at the ends of their tethers, they had beds in tents in the parking lot and we were on the brink of true catastrophe at levels approaching Italy, but only in certain places. I think the lockdowns that helped alleviate those situations, which they seem, in fact, to have done, were necessary. In retrospect, they were probably too generalized, but did they work? I *think* they did and in a year or two, papers from epidemiologist and economists will probably tell us.
The question is, how much of those lockdown periods and places met those conditions? Early on we looked at lockdowns as a way to stop the pandemic. If we had wanted to do that, we would have needed lockdowns like the ones in Wuhan, which seem to have been quite effective and also what we consider gross violations of basic liberties that would not have been tolerated in most OECD nations.
But lockdowns to keep the medical system from collapsing are another thing. I think they have worked and that last, more targeted Regional Stay at Home Order in California seems to have taken the pressure off hospitals. I know one friend of mine said they had to watch a guy with a heart attack die in her hospital because they did not have a bed. She said that it would have been an easy save if not for Covid.
Then there is the calculation of how much a life is worth. The US government says a life is worth $10,000,000.
https://www.npr.org/sections/money/2020/07/17/870483369/your-life-is-worth-10-million-according-to-the-governmentAbbreviated version of the above
https://www.npr.org/2020/04/23/843310123/how-government-agencies-determine-the-dollar-value-of-human-lifeThat's the number they use for enforcing health and safety rules. In other words, if a safety measure (tethers while working on scaffolding) costs $9,000,000 per life saved, the government says that rule should stand and if it costs $11,000,000 per life saved, it should go. It doesn't account for age. That's the theory, though things like car seat requirements and rear view cameras prove it's not evenly applied.
So when epidemiologist crunch all the numbers on the impacts of lockdowns and economists crunch all the numbers on economic loss, we'll know what was and wasn't "worth it."
But the answer will be complex, not simple. Looking at it as simple relationship (deaths :: lockdowns) and a binary (worked/didn't work) is great for polemics and terrible for understanding.
As is typical of all US politics these days, it is more important to score a win for your team than to figure out what good policy would look like. Were some lockdowns a foolish waste of human energy? I bet they were. Were some lockdowns essential to prevent catastrophic collapse? I bet they were. In a system where scoring for your team is less important than coming up with good policy, we would be focused on figuring out which were which rather than getting reelected or weathering a recall movement.