No mistake at all to my mind, if such an insane & illegal 'Pattonesque' proposition had been followed then god knows how much longer the fighting could have continued, or the eventual outcome.
Besides that, try motivating populations that had endured the loss of life, both public, and to people they knew, economic collapse, social privations, camp revelations, nuclear weapons etc. etc. of up to 6 years of war to join an attack on a recent ally and continue the joys of warfare. It'd be beyond Political and ethical suicide.
The cold war was a mess, perhaps an inevitable one, but as in all Politics, something of the 'least worst compromise'.
I hope that doesn't read too harsh a reply

. I have something of a Pavlovian response to the old "Now we start on the Russians".
Your cat made my pigeons flutter

.
Cheers,
Adam.