Why didn't they do that IOTL?
Russian war planning was much debated and goes through many changes before the war. After the Manchurian War, Russia's planning is defensive and extremely pessimistic. Danilov's idea prevails and extreme caution is the rule of the day. He fears all kinds of coalitions- Sweden and Romania joining the war against Russia and France being neutral. He favors a northern offensive against East Prussia and assigns four armies to it not the two Otl.
Alexeseyev is more optimistic school. The political and military situation changes for the better for Russia as well. By 1912, Alexeseyev is arguing that Romania and Sweden are unlikely to join a war against Russia, that British entry was likely and Italy would be neutral in a war with France. This opened up more possibilities. Alexeseyev also correctly argued that an attack on East Prussia was full of dangers (the Russians are defeated more by geography than the germans) and unlikely to yield decisive results as the Germans could retreat behind the Vistula. Austria was far more vulnerable
The main criticism of the plan were:
1) The north would be vulnerable. Alexeseyev deployed 13 divisions to the north versus OTL 29. He argued that this would be enough to defend against a spoiling attack from East Prussia. There were doubts about this especially if the Germans deployed the upper limit of 20-25 divisions to East Prussia.
2) The Russians also understood the need to draw the Germans off the French. If France collapsed early, which many in Russia expected, then nothing that is accomplished in the South would matter.
In the end, the Russians adopt a hybrid of the two plans. It leaves both the north and the south with too little to accomplish a decisive blow. The Southern strike fails to encircle and destroy the Austrians and the Northern armies are too small and destroyed. The four divisions the Russians draw off the French probably wouldn't have mattered anyway.
Knowing what we do now, we can say if the Russians had adopted the plan:
They would have saved the 1st and 2nd armies from destruction and probably obliterated the Austrians. France would have still survived and the Entente in much better shape. If the French had stuck to plan XVI or XV the two plans would have worked beautifully together. The war would probably have been over by September
@wiking
With the Russian 1st and 2nd armies intact and the Austrians destroyed, may I ask where all these German troops you are using are coming from