2) "Could be criticized" ... well of course that is true. Statistical analysis, coupled with the known physics of the greenhouse effect is pretty solid.
Those are two unrelated things. i.e. paper making claims about the influence of climate on storms can be complete nonsense even if the basic physics is correct. I call this kind of lazy thinking the 'bait and switch'. i.e. people take something that is well supported by science and then use it to claim that unrelated claim must also be true. It is nonsense. Science does not work that way. Each claim is evaluated on its own merits.
The best criticisms have been accepted but they didn't turn out to be true.
You can't prove a statistical analysis is false unless you can do experimental replication. All you can do in climate science is criticize the methods which is a purely subjective exercise. That is why it is so easy for alarmist scientists to dismiss skeptical papers. There is always some quibble that they can use as an excuse to declare it "debunked". The fact that their own papers have similar issues is shamelessly ignored.
Theoretically that's true but your example isn't really applicable to real life - no two papers could have completely symmetrical flaws in that way.
You miss the point. Someone claimed a skeptical paper was wrong because it did "curve fitting" but the same criticism applies to almost every paper produced by alarmists like Michael Mann but his papers are taken seriously. The only difference is Mann supports the alarmists narrative so his crappy statistical methods are ignored. It is a painfully obvious double standard.
I would look at the few papers published by climate scientists that DIDN'T agree with the consensus. The publishers weren't pilloried as far as I can tell.
We don't know what goes on behind the scenes but scientists like Judith Curry and Robert Pielke have talked about the abuse they received from colleagues for talking a less alarmist approach. Both decided to leave the field rather than put up with it. You, of course, will argue that they are lying or not representative but you have no evidence to support that belief. I am saying that they are credible enough that their claims of inappropriate pressure should not be dismissed and we should want to have some external authorities investigate how bad it is really is. There is the story of skeptical scientist that was sacked by his university for daring to dispute the alarmist narrative. The university claims his views had nothing to do with it but a court dismissed all of the universities defenses as nonsense:
https://www.abc.net.au/news/2019-04-16/jcu-scientist-peter-ridd-sacking-unlawful-federal-court-judgment/11021554 I know of a few - and will look that up when I can.
The problem is the chill in the current environment that could lead to paths of research being dropped as soon as the academic realizes it would be impossible to get it through the alarmists who are the gatekeepers at many journals. We can never know if these paths exist or not. We can only know is that if these did exist we would never hear about them because academics have a strong incentive to self censor. That is why I think more skeptical papers would mean we have more confidence in the consensus. As it stands the number of skeptical papers is simply too low to justify given the uncertainties inherent in the methods available to climate scientists.
5) Your thinking on this presumes that papers exist that are valid, and that are being shut down.
I am saying that your claims of absolutes (valid or not valid) do not apply when dealing with complex statistical methods applied to dubious datasets. All papers are flawed in some way. Why should alarmist papers be taken anymore seriously if these flaws were show stoppers?
Your closing paragraph unfortunately endears you to me as reasonable so I will have to shake that off as I search for the papers above and the (loud sigh) Climategate papers... (secondary sigh)
I would not spend a lot of time on that. If a skeptical paper has been published I have probably read about and am aware of the criticisms. Sometimes I even agree with the criticisms. My pet peeve is with the extremely bad alarmist papers which are treated as gospel because they support the narrative. I would he happy if people would learn to understand the limitations of the methods available and the kind of certainties claimed are not legitimate.