Yes, if you are a country that only wants to protect their homeland, cutting your ground forces as a result of nuclear bombs and ICBMs is perfectly rational.

Say that you are a citizen of a country endlessly threatened by invasion from a foreign power. Is it more important for you that your country has the nuclear bomb, which means your likelihood of being turned into glass falls from 50% to 0.1%, or that your country has greater control of agricultural production, meaning that in case of disaster you won't have to pay fortunes for imported food and cut your consumption? I'd say in this case the nuclear bomb is more important.

Also, we didn't see End of the World level nuclear destruction of any country because all the great world power developed the Nuke. The US Army very seriously considered using nukes in the Korean War as well as had plans for the invasion of the USSR (See : Operation Unthinkable and Operation Dropshot). The only reason these plans weren't carried out is because the USSR and China sacrificed very heavily in order to develop their technology and achieve technological parity with the West.