So, Alderaan was a legitimate military target. Was the level of force used against it justified? It’s a tricky question, but it seems the least bad of all the alternatives. Consider another option the Empire could have taken: invading Alderaan, removing its leaders and installing a pro-Empire regime. However, putting boots on the ground in this manner would likely have destabilized not only the planet but also the entire region, creating a breeding ground for religious terrorists and draining blood and treasure for decades. It’s not hard to imagine a Jedi State of the Alderaan System (JSAS, for short, though they’d likely prefer the simpler Jedi State (JS)) arising from the ashes of some ill-conceived invasion and occupation.
This was probably just the sort of catastrophe that Grand Moff Tarkin was trying to avoid when he devised his Death Star-centered defensive strategy. The Tarkin Doctrine, discussed here, is one based on deterrence and the threat of force rather than the use of force. Granted, you have to use force once for the threat to be useful, but it’s easy to see the appeal of such a tactic, which is designed to save lives in the long run. Imagine the human toll — not to mention the enormous fiscal cost — of launching invasion after invasion of breakaway systems. The utilitarian calculation is complicated, but it’s not hard to imagine a scenario in which fewer people died as a result of the destruction of Alderaan than would have died in a series of costly invasions.