Grant's star wasn't shining too brightly in Washington DC in March of 1863. He had just survived, by political influence, from being kicked out of the army over his near defeat at Shiloh less than a year before. Since that time he had tried at least two expeditions to take, or circumvent, the Vicksburg defences and these efforts had failed for a combination of reasons. So your suggestion that Grant was the only general who could have accomplished the taking of Vicksburg would not have been appearent to the higher-ups in Washington in 1863.

It would seem illogical that the military importance of Vicksburg was sufficent to offer Grant a promotion to take it when the practise at the time was to replace ineffective general with someone else. Most likely this was a veiled warning to Grant from his political backers through Halleck, saying "we stuck our necks out for you and pulled your fat out of the fire, now get moving and take Vicksburg!"