Whether it works or not, it's a waste of money
"Our Type 45s will have no serious ability to strike targets ashore, and we will continue to have no capabilities against ballistic missiles."
...and the absence of such capabilities for the past three years has been a huge problem for the UK because... how exactly? The thing is already three years late, and in the meantime we've been vulnerable to... what?
That's right: bugger all. Because we don't face any threats that these things would be useful against. It's time we stopped acting like the French, pretending that we're still a global force that needs to project military power to protect its interests around the world.
It doesn't matter one gnat's cock whether we put Aegis, PAAMS, or cardboard tubes painted white on our Type 45s, there's no conceivable scenario in which we will ever use this thing for it's intended purpose. Even in the remotely unlikely event of a conflict with Russia or China, it's highly improbable that the Yanks would not be involved -- and the last time I checked, their navy was as large as every other navy in the world put together, making our pathetic little flotilla of T45s rather irrelevant.
Just like every previous generation of military hardware since WWII that has been requested, designed, prototyped, built, delivered, commissioned into service, wheeled out for regular training exercises, decommissioned, mothballed and scrapped without ever being fired in anger, or at least in any action remotely useful to the British taxpayer*, the T45s will plough the oceans for a few years before finding their way to an Indian breaker's yard without ever having fired their missiles at a real target.
Like Eurofighter, main battle tanks, Trident (and before that Polaris), the whole thing is an exercise in technoporn. All we really need these days is effective air defence, inshore patrols, and an ability to keep the Channel and the North Sea open to shipping in the event of a conflict with, say, Guernsey or the Faroe Islands.
*No, I don't consider two Iraqi wars or our last fling of colonialism in the Falklands to have been worthwhile exercises.