>If this is true, why is it when showing a chart of data it is almost impossible to pick when any of these measures went into effect?

Quite exactly the opposite is actually true: it's always very clear from such charts that the measures are very effective.

Some examples:

https://www.canada.ca/content/dam/phac-aspc/images/corporate...

https://www.nejm.org/na101/home/literatum/publisher/mms/jour...

https://coronavirus.jhu.edu/data/state-timeline

Doesn't take "PhD level math" either, just some basic understanding how the effects are delayed by incubation period, testing and reporting, and how an exponential function changes shape as the exponent changes

It's not nearly as straightforward as you're pointing out because people voluntarily change their behaviour in response to circumstances, like case numbers, deaths, etc. Your big assumption is that top-down policies/controls are the biggest factor causing delayed change in numbers, but that isn't at all clear from the data alone.

I was arguing against the ridiculous claim that measures don't work at all. Whether they are voluntary or top down policies does not really matter.

amazing how in many places the cases start dropping the instant the lockdown comes into place, or sometimes even slightly before, rather than ~10 days afterwards as would be expected from the incubation period. can the virus hear us?

Incubation period varies, and is probably best modelled as a Gaussian function.

Some cases will incubate nearly right away, and others will take more than the 2-3 weeks that are often used as quarantine periods. Getting to the 95th or 99th percentile is not the same thing as getting to the 100th percentile.

This is one of the reasons that a covid-zero strategy is effectively unimplementable.

Correlation does not equal causation. And of course studies done by people with a vested interest in proving all this worked will say this worked.

You’d be hard pressed to find studies that say none of this worked. Such researchers would destroy their careers and be labeled as kooks.

So basically, you just don't want to believe the evidence, don't have any substantial criticism either, just vague bullshitting.