It did, sort of, in 1758, removing Copernicus and Kepler from the index and allowing free dissemination of all heliocentric books except Galileo's. That remained on the index longer, probably because of sour grapes. It is a pretty arogant and insulting work.
Answer: it wasn't about any lack of evidence. It was about contradicting Church dogma.
Sorry, but that doesn't square with the historical data either. Copernicus presented his model in Rome, to clerics, several times and sufferend no repercussions. Until Galileo's time, his book received no censure, and his Bishop was the one encouraging him to publish it.
Fortunately, the men currently at the head of the Church aren't so anti-science as their forerunners.
The Church was never anti-science. It overreacted in response to Galileo, but that's about the only example in which the Church even comes close to being anti-science.
Giordano Bruno. Yes, his case can be argued both ways, but still ...