Because a nuclear-powered missile can in principle fly in circles at low altitude off your enemy's shores for months at a time without landing or refueling, ready to be called down at any time with no detectable warning.
Well, if I am your enemy, I sure as hell won't let your missile cruise around my shore for a month
The difference between rocket fuel as a power source and nuclear radioactive decay as a power source is like comparing C4 explosive and a log fire in your fireplace. Once it great for providing a huge, fast release of energy, the other is great for providing a slow, steady release of energy.
Cheaper, easier to mass produce, doesn't need an unusually special launcher, hard to distinguish from air to air and other defensive missiles, easier to disguise the number of warheads waiting in readiness, can take an indirect/stealthy course, hard to shoot down, can include smart tracking for moving targets like carrier groups.
Maybe so it can double as a shitty nuclear bomb. I'm gonna crash my small nuclear reactor into you.