Why was Nobel Prize given to Baeyer for his "faulty" Baeyer's Strain Theory?
Scientists are human beings after all. Nobody gets a Nobel Prize for inventing a "formula". It is the idea that makes an impact and new ideas are respected. Scientists like normal human beings make honest mistakes, but try their best to be correct. The guy who got the Nobel Prize in polarography, Hervosky, in the 1950s made errors in other electrochemistry papers, does this mean the prize be snatched back from him as well? Max Planck when he derived his blackbody radiation law, he did not believe much in atomic/molecular theory (later on he changed his views). He also received a Nobel prize.

If you read the citation/biographer by the Nobel Prize committee, the award was not due to some cycloalkane strain angle but the prize motivation was "in recognition of his services in the advancement of organic chemistry and the chemical industry, through his work on organic dyes and hydroaromatic compounds."

The Nobel Prize clearly says "Von Baeyer’s work was at once pioneering and many-sided. With admirable penetration and extraordinary experimental skill he combined dogged perseverance and, even at 70 years old, a youthful buoyancy in his work. He was careful never to overestimate the value of a theory. While Kekulé sometimes approached Nature with preconceived opinions, von Baeyer would say: “I have never set up an experiment to see whether I was right, but to see how the materials behave”. Even in old age his views did not become fixed, and his mind remained open to new developments in chemical science." (https://www.nobelprize.org/prizes/chemistry/1905/baeyer/biographical/)

You can see here, (good) scientists are open to change and are willing to listen to others. I found very good scientists to be very humble (with a small fraction of outliers), but only the mediocre ones are at times rigid and arrogant.