Yes, but it doesn't really disprove the assertion that lockdown's work. It more proves that the other approaches they tried either dont work or weren't applied effectively.
There is plenty of evidence that lockdowns do work. Whether they make sense from an economic or overall quality of life perspective is a separate issue. But they work.
I think you're misinterpreting my comment. I'm not saying lockdowns don't work. I'm saying that there is no evidence that lockdowns that contain exceptions for school aren't significantly worse than lockdowns that include schools.