The problem will be the same, if they stop Control in the present (the how does not really matter) it will not exist in the future to send back that probe that attacks Pikes shuttle which is what triggers all of this along with the anomalies.
Like I said its a loop, defeating Control in the future is no good as its already won, the only option is to do it in the present but in doing so all of its future actions will never have happened thus triggering the reset.
The only way around that is for Burnham to take those actions in the future that Control would have done before it was denied the data and defeated, like send the probe back to attack the shuttle and compromise Airiam, Burnham would have to knowingly sacrifice her friend and kill all the personnel of S31 plus the Admirals.
Then again even that would not be enough because Burnhams mother would also have to agree to play her part such as using the suit and coming back in time to tell everyone that all organic life has been ended when in actual fact it hasnt.
Could Burnhams mother be lying to ensure there is no reset, it would require Burnham to send that probe and sacrifice a lot of lives if so.
Hence why it would just be simpler and cleaner for Burnham to take advantage of the suit, go back to before her mother approaches Leland about the time suit and undo all of it, she could also tell Leland that there is no need to worry about the Klingons as the time crystals are in safe hands and always were.
Burnham would grow up with her parents, Spock would never have a sister and the Klingon War would never have happened at all.