Not an expert either but Sagittarius A* has a mass of 10^6 solar masses, the Milky Way itself has a mass of approximately 10^12 solar masses. So I doubt that Sa

Not an expert either but Sagittarius A* has a mass of 10^6 solar masses, the Milky Way itself has a mass of approximately 10^12 solar masses. So I doubt that Sagittarius A* is even relevant in terms of the Milky Ways gravitational potential. That said, the existence of Sagittarius A* does (most likely, this is an area of debate) have an impact on the Milky Way due to the strong, high-frequency radiation from its accretion disk, which affects the gas surrounding the central region of the galaxy. Still, this is probably not an incentive for anyone to destroy the black hole (if that were technologically possible). In addition, keep in mind that any galactic-scale effects take on the order of millions of years to take place. (With supernovas or other super high energy events being an exception) So my intuition is your novel would need to ignore a few physical facts, but its fiction after all :D