~1500 multiple warhead weapons is still enough to blow up the world several times over,
No it's not. The very idea is preposterous. Blast radius of a 1mt Minuteman warhead is about
Making up numbers are we? The destruction radius of a typical 400 kT modern warhead (urban airburst) is actually larger than the "4.8 km" you pulled out your nether regions for a 1 MT warhead. Far from being "absurdly unrealistic", your urban destruction radius is actually a low-ball. In a nuclear urban annihilation attack (multiple warheads against large cities) a destruction radius of 7 km is reasonable (anyone outside is fatally burned, buildings are damaged enough to serve as efficient furnaces as the multitude of set fires merge into a fire storm).
This gives us an urban area destroyed of ~150 km^2 per warhead, or a total of 225,000 km^2. This is not the whole world, but it is about half of the world's total urban area with populations larger than 500,0000 numbering 2 billion people. Such an attack could easily destroy the world's entire petrochemical processing and storage infrastructure in a single stroke, as well as all of its major ports. Half the urban population in the world dead all at once. No oil or food shipments for anyone, anywhere. A billion deaths is just the starting point. How far would the population fall through famine and disease until it stabilizes?
Not the "end of the world", but the "end of the world as we know it" for sure.