I'm not an expert on the issue, but I hear a lot of things from people who claim to be.
Personally, I see that we (the US) use the heck out of them in our current wars. And the BBC article misses a couple of points, I believe.
In addition to being a mobile launching platform for attack, the AC is also a good platform for high-quality realtime local aerial recon, both fixed wing and helicopter type. In addition to putting bombs on the ground via fighter/bombers, Naval air can put boots on the ground, as well as being a vital link in supply lines and medical evacuations. This applies also to peacetime missions, including supplying humanitarian aid or evacuations of civilians. And, unlike a stationary air base, an enemy attack has to find it as well as hit it. The Six Day War comes to mind as a good reason not to have all one's flying assets on land-based airfields.
I don't know how many we need, but I do think they still serve a very useful role.