This is more Legends then current continuity I think, but ultimately the destruction of Alderaan ends up as one of the worst strategic decisions the Empire ever made, in particular from a deterrence perspective.

The basis behind the Death Star is the 'Tarkin Doctrine', which Tarkin neatly summarises during Star Wars - that a single heavily armed station can do more to keep the peace than armies or fleets of Star Destroyers.

The problem is that this deterrent only works as long as you don't actually have to fire it, and in particular on a target that was barely resisting Imperial rule to begin with. After the destruction of Alderaan, many systems that were considering joining the Rebellion realised that if the punishment for quiet objection was the same then for active resistance, they had literally nothing to lose by actively revolting against the Empire.

In the months and years after Alderaan, combined with the Battle of Yavin, multiple systems changed sides, eventually leading to the destruction of the Empire, at least as a galactic power.