Fair enough. It will be next to impossible for the Americans to invade all of Russia. This is something which even Napoleon and Hitler couldn't achieve. If the Americans attempt this, then there will be tens of millions of American casualties, without any good results to speak of.
I agree, that world peace is at best guaranteed not by words, but by power balance. And with the level of technology at mankind disposal, that means mutually assured destruction (MAD).
To continue to deter in an era of strategic nuclear equivalence, it is necessary to have nuclear (as well as conventional) forces such that in considering aggression against our interests any adversary would recognize that no plausible outcome would represent a victory or any plausible definition of victory. To this end and so as to preserve the possibility of bargaining effectively to terminate the war on acceptable terms that are as favorable as practical, if deterrence fails initially, we must be capable of fighting successfully so that the adversary would not achieve his war aims and would suffer costs that are unacceptable, or in any event greater than his gains, from having initiated an attack.
— President Jimmy Carter in 1980, Presidential Directive 59, Nuclear Weapons Employment Policy
The doctrine of MAD was officially at odds with that of the USSR, which had, contrary to MAD, insisted survival was possible. The Soviets believed they could win not only a strategic nuclear war, which they planned to absorb with their extensive civil defense planning, but also the conventional war that they predicted would follow after their strategic nuclear arsenal had been depleted. Official Soviet policy, though, may have had internal critics towards the end of the Cold War, including some in the USSR's own leadership.
"Nuclear use would be catastrophic."
— 1981, the Soviet General Staff
Russia is at an advantage in having spread over a larger surface area when compared to the United States. The total surface area of Russia is almost 2.5 times that of the mainland United States.