Screw the man-made disasters, just think of how fast diseases would spread. IIRC, dense population centers were one of the contributing factors to the bubonic plague.
Another contributing factor was the lack of modern medicine. Plenty of communicable diseases exist today, and residents of dense neighborhoods are doing fine. If a disease kills too fast for a treatment to be discovered in time to prevent many deaths, it will probably be killing too fast to spread effectively. Swine flu killed ~14,000 people worldwide, so I'd put dying from an outbreak of a deadly disease at the same level of probability as a man-made disaster like terrorism. In other words, not likely enough to be of much concern.
NH is pretty big compared to the effective range of a nuke. A typical nuke in the middle of NYC wouldn't even destroy all of Manhattan, let alone kill everyone in NY. It would take a lot of nukes to carpet-bomb all of NH.
You just need to lay a few down the west side and wait for radioactive winds to take care of everyone else, but yeah, you have a point. I think most people vastly overestimate the blast radius of nuclear weapons.
A 1 megaton nuclear bomb detonated near the surface has a blast radius of about 1.7 miles. Pretty much nothing is left within this circle. Meaningful lethal damage only continues out to about 2.7 miles.
A 1.7 mile radius translates to roughly 9 mi^2. A 2.7 mile radius is roughly 23 mi^2. To carpet bomb New Hampshire, you'd need a lot of nukes. About 988 of them in fact.
Now 25 megatons is more interesting... you'd need about 68 of those to ensure <2% survival rate, or 25 of them if you are satisfied with <50% survival rate.
Of course, with good placement and strong winds, you could effectively kill 99% with only about 12-15 one megaton bombs. All that radioactive dust from the mushroom cloud comes down somewhere, and with a 15mph wind, that means a lethal dose within 90 miles of ground zero,
Even with the UK's very limited nuclear arsenal (compared to the US and Russia) it would be capable of wiping out the whole population of the US using its American-sold MIRV's.
One nuclear launch can easily land well over a dozen nukes with considerable tonnage.
The real question is what's more cost effective 1000 1-megaton nukes or 70 25-megatons? 1000 megaton total vs 1750 megaton total.