I did have years ago somewhat of a class about scientific approach.
Nothing deep, just quickly stuff and I forgot a good portion of it.
The big thing about classic physics and Newtonian physics is that a lot of the experiments were cheaper, and, different then it is from humanities and bios, they are supposed to work a 100% of the time, and if they dont, it is basically the experimenter's fault or fault of instruments. So, basically, these "primordial" scientific experiments could be replicated hundreds of times. This is the "hardcore" part of science, that is indeed rigorous, as mostly physics and chemistry are. And that is a quick and simple yet superficial way of explaining the "scientific method" and how it should be: Different and independent sources replicating the experiment.
However, with time experiments got expensive and expensive, and where some experiment were just basic mixing chemical stuff and observing colours, particle experiments went by and these can only be done like... One time in a decade in only one place. And, of course, later bios and then humanities followed by and these cant really keep up with the rigorous standards that earlier chemistry and physic could come by. While if you throw a stone in your open window to a clear place it will fall a 100% of the time, if you go for even the 'best' versions of MBTI tests the test-retest rate will be only 60%. A lot of medical experiments are on the middle zone: They get a better repeatability than MBTI but less than Newtonian physics.
With that in account, I do agree that the peer review as described in the link by the OP isnt rigorous as it should, but I think people might be confusing a few things here. Im sorry if it sounds a little arrogant, but physics and chemistry, at least in terms of experiments, are above all other sciences. Not necessarily because people on other sciences are incompetent, but due to repeatability. So, in one extreme, comparing Newtonian physics with MBTI, taking a few failure experiments and procedures from the medical department does not cancel the whole science and make it less scientific and "yaaayyy, science isnt like that, lets pay attention to stupid conspiracy things and pretend we are rational". Things arent black and white like that, it pretty much depends in which part of science you are talking to. If it is MBTI that barely or perhaps not even make it, or Newtonian experiments that have been replicated literally thousands of times (correction: Actually, Newtonian physics doesnt work properly on particle physics and objects close to speed of light, so it doesnt work a 100% of the times, but it will in normal size and speeds that are slow when compared to the speed of light).
Repeatability is indeed the most appropriate way and it would be indeed the best peer-review; But it gets too costy sometimes. Because of that, liking or not, like many things in life, honesty, sincerity, is something of vital importance. At the same time that a country, regardless of having a small state or a big state,
is very prone to succumb to internal dishonesty, soft sciences are very prone to dishonesty as well. If people want to fool for money, for prestige, whatever... It will indeed ruin things. I dont think there is really any truly objective solution to this, but there is integrity. This happens somewhat to data analysis as well.