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Pretty much agree with what you said.
Yes, I guess the article does, thanks for sharing it. I'm neither from a science background nor any kind of investigative journalist, so it's probably all above my pay grade. However, in an attempt to answer: Do these kinds of rankings matter? I'd say only to the extent that rankings beget funding and serves as PR.
As you say, it's better than flat out rejecting science, and I do agree with that. But it's not a dichotomy of any sort that we need to do that, nor do we need to throw our entire (pre and post electron microscopic) epistemological framework out of the window. I feel that what I have seen come out of (more) authoritarian states lately, is the inculcation of scientific progress, and this is questionable. My skepticism is more related to nuance within the application of science (as opposed to experimental.) What some in the more philosophical fields see as overspecialization, at an expense of rejecting a more general overview of how nature itself works (and the need for it to be applied.)
What did the late General Mao say, something akin to (political) power comes from the barrel of gun? Well, obviously this may be true but ~70 years on, I'd posit that power also comes from consistent messaging that the pursuit of scientific knowledge and rationalization of irrational objectives is the end all be all of life. I feel we see this very strongly in pharmacology today, in that, when it becomes a hammer, everything looks like a nail.
Sorry, I probably went on a tangent. Obviously P.R.China, is very much on the cutting edge with regard to many scientific areas. and I agree that the publications such as Nature tend to skew these rankings (according to their major sponsors' wishes)? As @SimpleStacker pointed out scientific prowess is becoming increasingly co-opted for economic and political advantage. As with regard to Harvard, I find that a private institution, asking for public finding is entirely unethical.