It's not quite a nuclear HEAT warhead. Normally in space a nuclear explosion would just emit gamma rays in a sphere. A Casaba-Howizter traps those gamma rays in a beryllium radiation case, directing them through a hole into a propellant plate which vaporizes it into a high velocity plasma jet.
So most of the energy of the explosion is directed towards the target, and the jet is very narrowly focused so the warhead can be detonated from much further out, so the missile doesn't have to cross the innermost point defense zones where laser PD becomes exponentially more effective.
The PD argument isn't all that relevant in Star Trek specifically, but the standoff range also means the missile can cope better with any evasive maneuvers.