1) Why put humans on warships at all? Algorithms are probably better at it. Computers would obviously do the heavy lifting anyway (calculating burn times). An algorithm knows no fear, shows no mercy, and does not flee or surrender unless programmed to do so. The only thing left is target selection, and it doesn't seem worth bringing a human along just for that.
2) If you don't need to put humans on warships, then you quickly realize you don't need a warship at all. Just send a bunch of missiles from wherever the warship would have launched. It's harder to take them all out at once with a "mine" or something. You also get to build more missiles if you don't need to build the warship. Sure, you might attach a collective nuclear rocket "booster" to many missiles to build that initial velocity. There's no need for that rocket to be anything more than an engine temporarily attached to the missiles. It's also not really required to begin with.
3) If you're sending lots of missiles, there's no reason for them to be any larger than the smallest size permitted by design and manufacturing practicalities. For something that amounts to a liquid-fueled rocket, that smallest size is preposterously small. A liquid-fueled rocket can be fit into an object the size of a soda can with current technology. This makes the notion of point defense completely laughable: divert ten thousand missiles out of one hundred thousand, and you've reduced the incoming energy by 10%.