Even without the Reapers on the scene, being home to the three war-faring races of the Humans, Krogan and Turians, the Milky Way galaxy would explode in a horrible cloud of war and savagery within a year of the Asari being wiped out. For the most part what's keeping the galaxy from slaughtering each other is the Asaris' strong economic and political influence, teamed with their wisdom, patience and aversion to warfare.
Yes, they kept the beacon to themselves. And yeah, they used it to give themselves a technological edge. But what they didn't do was use it to keep the rest of the galaxy down. If it'd been the Turians, Humans or Salarians in their place, it'd likely be a very different story.
So yeah, I could be pushed to sacrifice any race (humanity included) to save the galaxy, if the stakes were that high. But if it were the Asari, I really don't think it'd be 'saving' the galaxy for very long.