What hypothesis are the data meant to test?
Is it, "In the absence of human activity, climate is invariant"?
Is it, "Past swings in climate were caused by something else, THIS one is caused by humans"?
Really. What is it?
Good points. Lindzen’s view is that there is a most likely a small amount of warming due to man-made (anthropogenic) carbon dioxide. Whether that amount of warming is a net benefit - if it even exists - or detriment is not clear.
Hypothesis testing is not necessarily useful, this is not grant writing, and there is no obvious “signal” or test statistic that can be used to verify or refute these claims.
The best signal would be the mid latitude winter atmospheric thermal profile, and in this case the evidence is completely lacking. There is no signal. If global warming is occurring due to carbon dioxide, the models have got it all wrong, because their mechanism does not occur in the real world.