For that you need a synthetic aperture radar and a highly maneuverable hypersonic missile. Aircraft carriers are surrounded by other ships and have air wings flying air patrols. If you paint an aircraft carrier with SAR you're likely to eat a couple AAMRAMs or SM-3s.
With a hypersonic missile it needs an explosion big enough to disable a carrier within its CEP radius. The most likely warhead capable of that would be nuclear. So you've just started a nuclear war with the United States.
I actually started thinking about the carriers a couple of hours after I had made my comment, which is to say I think that you're of course pretty on point.
Hopefully that danger that you hint to will make the smart people still left in the US Military think twice or thrice when it comes to continuing the aircraft carriers policy, as they've become too big of a target and if the US will need space-based laser guns (or whatever it is that this article proposes) in order to defend them then something is most certainly amiss.
You (and the article, frankly) are pointing them at the wrong targets: the best application of hypersonics is to shoot them at the US's blue water navy. The combination of perfect, real-time information via synthetic aperture radar and highly maneuverable hypersonics turns an aircraft carrier into an extremely expensive floating coffin.