In an ideal world this could work, but Bet is far from one. You're assuming that just giving magic to a bunch of people would miraculously stabilize the system, rather than the new mages being swallowed in it and just making the chaos several degrees worse.
And even if the eventual outcome was for the positive, the sheer loss of life the process would take is just insane. When you propose blanket-giving magic to the world, you're also rescinding the ability to choose who gets it; be they perfectly normal civilians or horrible monsters: Gesellschaft, the Yang-Bang, Accord, the russians that shot Behemoth, the African warlords, the dictatorships in South America and generally corrupt people like Calvert.