Not surprised to hear about Cochrane's results. The science does smell funny. I read a bunch of hypertension papers this last year (I have a home machine and wanted to know how to interpret the results). Beyond the fact that inter-reading repeatability is very poor and a lot of the explanations are very ad-hoc ("fear of doctors" etc), there are other issues.
First problem: natural variance across healthy people is huge. Doctors have a target they think everyone should hit but it's just a gross average, they don't seem to take into account the possibility of genetic variance at all.
Second related problem: it's common to be told what a healthy BP is for an "adult" although BP averages for men and women are quite different, and BP is also heavily affected by age (controlling for health).
Third problem: correlation is not causation. It's a cliché because it's a real issue. The public health community is prone to blurring the line between "two variables are found to be related in a study" and "one therefore causes the other" without doing the work to prove causality, and when I went looking for what studies established BP->cardiovascular disease causality it was remarkably hard to locate firm evidence. It could easily be the other way around. Indeed in most hydraulic systems it's understood that pressure is the result of other mechanisms and under/over pressure is the result of malfunction in pumps or piping. In healthcare they argue it's the reverse: that over/under pressure is the cause of malfunction elsewhere. There's probably a circular relationship but all the material targeted at regular people makes strong claims of causality when the underlying literature seems far less certain.
Fourth problem: perhaps unsurprisingly given the third problem I found studies where people were put on anti-hypertensives and there was no improvement. Actually I read one study where the treatment outcome was purely negative: there was no effect on heart disease or other outcomes of interest but there were lots of patients who fainted due to excessively low BP. This study seemed reasonable well constructed but the negative outcome didn't seem to reduce the field's certainty in anything (a super common problem in public health). Doing trials like this is hard because any time anti-hypertension drugs fail to work it's interpreted as evidence that the damage was already done earlier in life thus requiring ever longer studies to detect.
Fifth problem: a lot of the underlying scientific claims trace back to one longitudinal study in a single village in Japan, done decades ago. It's remarkable how often you follow citations and end up back at this dataset. When you look at what the study did it's kinda sketchy and not particularly convincing, but because the BP->CVD link is hypothesized to be a very slow acting effect it takes a huge effort to collect data. The field seems to be caught in a loop where they exaggerated their confidence early, so now there is not seen to be much point in doing better studies because it'd take years (bad for your career) and why study something that's already "known".