That's the 'correlation = causation' argument. And in the case of the current lockdown at least, it didn't start to drop 'immediately after' - it actually started to drop before the lockdown could have had any effect.
A graph of deaths in Sweden compared to the UK was posted on here a week or two ago, normalised for population, and showed a pretty much identical trajectory for the whole of the past year. Also, comparing the Worldometers stats for European countries with the severity fo measures shows absolutely no correlation (the Stanford University study also looked at this), and a similar lack of correlation can be seen in the USA when comparing states in the same climate zone.
There is bound to be a correlation in this country because the lockdowns were imposed when the peak was being reached - and the argument that without the lockdown it would have kept going upwards doesn't really hold water.
"Correlation = causation" being the basis for the argument that the current decline in cases is to do with vaccinations, along with a natural variability that just so happens to see a decline at just the same time as the seasonality you argue as a prime cause of respiratory disease spread is at it's most significant.
A lockdown cannot have an impact in three days - so the peak was before it could have had any effect.
How do you explain the correlation with Sweden? or the fact that a Stanford University study has concluded that lockdowns have little or no impact?
A comparison which is valid when it supports one argument, yet not when you compare that paradigm against another, more local one?
As for the Stanford study (I didn't notice a link - do you have one so I know I'm reading the same thing?), how does that sit within the literature as a whole?
There seems to be a lot of relying on cherry-picked examples to support a contention that no form of NPI can have had any impact on Covid; something that is profoundly counter-intuitive when applied to a virus which spreads based on human to human contact.
Anyway, reverting to the topic, my gut feeling is that this plan is reasonable, attainable, and strikes a reasonable balance between optimists and pessimists.