The value (and biggest cost) of nuclear weapons is strategic.
It has been claimed that "A country with nuclear weapons cannot be defeated [at an acceptable cost], but it can be destroyed." This statement is not quite true -- witness the outcomes of the Korean and Vietnam Wars, and the fates of the Soviet Union and South Africa. But even in these cases, the defeats were via domestic "loss of will to fight", not via military occupation of the United States, Soviet Union, or South Africa.
It has also been claimed that the only truly sovereign states are those that control their own currency, borders, and nuclear weapons (capable of being delivered against any power that might attack the state).
Economies of scale
The cost to maintain and secure a military base with one ICBM is not very different from the cost to maintain and secure a military base with 25 ICBMs, with a total of 200 MIRVs.
The secondary nuclear powers have generally used joint ventures (and/or espionage) to reduce their research and development costs. (The British received a great deal of R&D help from the Americans; the French and Israelis had a joint venture; the Soviets and Chinese stole important technologies from the Americans; the North Koreans helped the Pakistanis, who helped the Iranians; et cetera.)
Low kill ratios
As Philipp and cpast have pointed out, there are practical reasons to believe that 200 nuclear weapons are more valuable than just 10.
Many ICBMs are stored in hardened missile silos, and/or can be moved around. If a nuclear warhead detonates "too far" away from the (real) target, it might not destroy the target. For hardened missile silos, this "too far" distance is a tiny fraction of the distance that the ICBM has to travel. Thus, if a country has 25 ICBMs, an opponent might need hundreds of warheads to be confident of getting a "close enough" hit on every ICBM silo.
Limits on the devastation
During the era of atmospheric testing of nuclear weapons, the total strength of hydrogen bombs that were tested was comparable to hundreds of modern nuclear warheads. The radiation produced was acutely dangerous in local areas, and caused cancer risks downwind, but the overall effects were dwarfed by many other man-made disasters.
The Earth is big. Suppose a nuclear war devastated a 15-mile radius circle around 1,000 locations. That would be about 700,000 square miles, including many of the world's most heavily inhabited and/or industrialized areas. But it is only about 1 percent of the world's land area. Huge amounts of military and industrial infrastructure would survive, including some very pissed off survivors of those attempted decapitation strikes. Anyone fighting World War III needs to be prepared for a long war -- it might not be over right away.