Socrates and Galileo are but two of the more recognizable names on an endlessly long list. That list being made up of individuals who were correct but had their views judged by the masses, and lost. Socrates was killed, Galileo was merely imprisoned in his house until his final breath. Science is an issue, like many others, that often struggles when you get into matters of popular consensus. New ideas which end up being correct after often vigorously fought against, particularly when they undermine science that others want to be true.

We wanted the Earth to be the center of the universe. When somebody published writings suggesting we're just another body of no uniqueness revolving around a similarly indistinct star it posed a typical issue. If a scientist wanted to advance their career, they could come out quite strongly against this. Coming out in support of it risked turn the mob's attention on you. Refuting invalid refutations of this view is a non-trivial matter. Refuting what might, in modern times, be thousands or more - would be impossible. Indeed Galileo's correct heliocentric view would not come to be accepted until many decades after his death.

Of course we've overcome such reactionary barbarism though, right? Today there are at least two major issues we face. The first is corporate science. To give a now recently resolved example consider leaded fuel. Leaded fuel is something that from its earliest day drew skepticism. Nonetheless it persisted for the better part of a century with government and scientific endorsements of its safety. This was in large part because the corporations profiting from it made sure to stack the science in their favor and to also vigorously attack any critics of its safety. In an open system you'd see the same problem as above. Support the science suggesting leaded fuel may be unsafe, face the well funded mob. Oppose the science, get grants, accolades, and personal recognition. Compare Midgley, who lives in sufficient infamy that only his last name need be referenced, to e.g. Alice Hamilton.

The other issue is one of social matters, very similar to the issues that Galileo faced. Genetics is a perfect modern example. As but one example there, the connection between genetics and intelligence is in no way ambiguous. But this is something we, socially, do not want to accept and so progress is absolutely glacial and if one steps a hair outside an invisible line that we've drawn, they risk getting condemnation, hate, and exclusion from the scientific system. In many ways this is exactly what happened to Galileo. He was not imprisoned for his views, so much as for his disregard for social norms when expressing them - similar as well to the story of Socrates, who was unrepentantly provocative til the end.

The problem there is that science should be judged based on merit, not on presentation or nicety. As you move more towards a social system I expect we'd begin to move ever more from the former to the latter. This would be magnified a million times over if we chose to use a pagerank style system as you proposed. I fully agree our current system is, at best, dysfunctional. But I think our idealization of social systems is quite often contradicted by what they turn into - something Socrates, quite prophetically, often spoke of.