The new government of German-Austria wanted union with Germany. It would seem that giving Germany the new Austria would serve as a decent trade for Alsace and the Polish Corridor and may have served to keep the peace. But the treaty of Saint-Germain explicitly forbade this. Why?
Shortly, because they didn't want Germany to end up with more territory than it begun the war with. Even with all the "self-determination" talks from Woodrow Wilson and the Allies, guiding various borders along post-war Europe, Austria was an exception because it would then give even more territory to a country the Entente was trying so fiercely to punish. Even though a large portion of Austrians were favorable towards the prospect of an Anschlüss, it was expressively forbidden in Versailles.
Source: The Coming of the Third Reich - Richard J. Evans