Yeah, Putler can nuke, but ruSSian ABMs are nowhere near SM-3, Aster-NT bloc.2, THAAD, GMD, etc...
You only need to protect your government, and super duper critical sites. For all intents, and purposes, even 1000 warheads will not be enough to even halve US military, and economic output.
They put 1000 warheads into military sites? Good! US has thousands of them, most only manned by less then a dozen men.
They want to "vaporize" cities? Besides top 10 cities, US has very small population density. They will need half the launch just to partially destroy them to render them unsuitable for continued habitation.
NATO is 1 billion people, and 1500 warheads cannot possibly kill more than 50M. Only 5% of population.
Russia, or China on another hand are super centralised countries. Officials there can't cook a pot of porridge unless commanded. Loss of the eunich class all living in imperial capital will paralyze the country. If eunichs are dead, or the party leadership along with them, it will take a few civil wars, coups, and a year+ of martial law to reestablish the most minimal semblance of control.