Does a nuclear missile need big accuracy?
If you're trying to kill a nuclear missile in a hardened silo in South Dakota, yes.
If you're trying to hit Chicago (which is where I live), not so much. You set off a nuclear weapon inside the city limits, it makes a mess.
However, the Chicago City Council has outlawed transportation of nuclear weapons inside Chicago city limits, so if the Russians tried, they would be in violation of city ordinances.
Did I mention that Chicago aldermen are idiots?
Yes. My answer assumes that it would be put to rational and effective use. The most rational and effective use would be to destroy something that conventional means would have a difficult time destroying due to range issues and hardening. For example, in order to destroy an enemy missile silo, multiple near direct hits would be needed.