There seems to be a bit of a hole in the CIWS capabilities of Western navies at the moment. Where the old gold standard systems are being phased out and a "silver bullet" kind of replacement has yet to appear. And it's difficult because the evolution of ordnance they're supposed to counter and the difficulties and costs associated with performing effective and realistic tests. So I find it hard to put too much stake in claims about hit rates and things like that.
What I do know is that both the Dutch and Korean navies are looking at replacements for the 30mm Goalkeeper with all manner of combinations of caliber's and missiles being considered. I also know that the Italian navy likes 76mm for close in defense and the Russians just put bunch of missiles and cannon together on a turret. Whether any of these solutions (or none of them) will prove suitable to counter future hypersonic or ballistic ASM's... we'll see (or not, hopefully). But there are some points I have with regards to the discussion above.
First, close in defense having it's own sensors seems like a plus to me. Nothing bad about having some more sensors on your ship, not only do they provide redundancy and relieve other sensors of those taskings. They're also just extra sensors in and of themselves, optical sensors and radars can be used secondarily for surveillance tasks etc. So having independent CIWS with it's own sensors seems like a plus to me.
Second, what the above discussion seems to disregard is that naval ships are at a certain place and time for a reason. It's pretty rare (except maybe for testing) that the reason is to sail out shoot down some missiles and empty it's magazines and sail on. Naval ships have missions, whether it's escorting or patrolling, usually they're going pretty far from their bases. So the assumption that situations where you need more than x amount of missiles are rare so lets not arm and prepare ourselves for that, are decisions that bean counters take weighing the lives of sailors against a budget. But realistically speaking more is better!
Maybe countering 30 or 40 missiles in an engagement seems like a rare occasion. But modern naval warfare (theory) is missile centric and who ever said that during your mission you'll only have one engagement? One commenter above mentioned that the 20mm cannon on a Phalanx is easy to reload. At the same time it's very difficult, if not impossible, to reload a VLS at sea. So if you fire 20 of your 36 ESSM in one engagement you only have 16 left for all the engagements you encounter until you resupply.
At some point it becomes not only a question of capability, but also of staying power.