Many times Star Trek has taken us to the future only to reset the status quo at the end of the story arc. Tapestry (but in reverse?), that time Voyager crashed in the ice, and all that.
How likely is it that Discovery went to a mutable future, just one of many, especially with the Temporal Cold War, Carl, Q, Trelane, Janeway, the HMS Bounty, and any number of other temporally active agents out there in time? How locked in is the 32nd Century?
We now know when, where, and how the burn happens. Therefore, it can be prevented.
They were destined to go to the future, learn about the burn, return and prevent it. The burn was never going to happen.