We disagree on what science is. I don't think I agree with what you mean by "guessing game" (if I understand what you are saying there). Science has a unique power to build technology, save and extend lives, predict weather, build satellite networks for instant global communications. Our modern society is built on and depends on science.
By institution I mean that our societies have built up a system for developing, storing and using knowledge gained by human endeavor over centuries. We have a system of mathematical notation that allows scientists to express ideas. We have an education system to maintain the knowledge over generations. We have peer reviewed papers, and scientific standards. And we have an ever increasing body of knowledge.
Perhaps most importantly we have a way to answer questions through experiment with accountability to a community of peers.
Yes, very few of us will enter this community... it requires 10 to 12 years of full time study in advanced math and previous knowledge including experience doing research and being reviewed by peers.
That is what I mean by "scientific institution". I wasn't saying that science was the institution... it is our societies' carefully built community of scientists with the legacy of centuries of building knowledge... that counts as an institution. This is the way our societies do science.
Modern societies ignore the findings or the scientific community at their peril; whether the issue is global warming, or GMOs.