How certain are we that Discovery went to THE future rather than A future?
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 know, but no Star Trek character which live before the burn know about it. The Discovery should go back in time for that, and it'll always be too dangerous.
True, but that can be said of a lot of atrocities in Star Trek history. Some of which are necessary for the preservation of the Federation as we know it.
The Enterprise C incident, for example. The loss of the ship with all hands (presumably) helped prevent an escalation of the conflict between the Klingon Empire and the Federation.
We also know that the Burn didn't create issues wholesale. All it really did was exacerbate the existing dilithium shortage by dropping the number of ships, but the underlying problems were likely going to happen either way. The Chain had the advantage of the Courier network, while the Federation was still using warp-drive ships trundling along at low speeds.
The only notable thing that did happen is the loss of functioning ships, straining Federation resources further, and that N'var believed that their experimental stargate network caused the Burn, so they stopped developing it, but the former would have likely happened anyway, especially if the Federation was to get into conflict with the Chain.