The problem with this and a fairing is that if the fairing catches the open side, it's going to drag behind like a giant parachute and take the plane down. The fairing is huge (13m long x 5m diameter), even compared to a big plane.
They considered doing that to reuse the Saturn V with a giant helicopter with rockets at the end of each propeller. It didnt go anywhere. Though people have been using air capture for more reasonable use cases, and rocket lab is going to be air capturing their electron rockets.
That was the original plan. But according to https://en.wikipedia.org/wiki/Vulcan_Centaur
they went ahead without funding it, though they may some time in the future. So for now Vulcan is going to have a disposable first stage, just like all the other old-time space rockets.
Apparently thats been considered, and you still might see another company like electron try it. It's just a bit harder to do safely and some other limitations.
One of the main reasons they aren’t doing it is that the fairing halves are so far out to sea (about 800km down range) that no helicopter could have the range with a fairing dangling down to make it back to land (the Sikorsky Skyhook, for instance, only has a range of 200nmi or so... maybe you could get a specialized helicopter to do it with heroics like drop tanks, but the cost would be much higher), so they’d need to land on a ship after capture anyway. By catching the fairing halves with ships directly, they save the substantial costs of also having helicopters.
Notice that with RocketLab reuse, the helicopter is staged from a ship at sea. However, probably can save more money by recovering a RocketLab Electron first stage than half of a fairing (you’d need one helicopter per fairing halve but only one helicopter for Electron... Electron also has a much smaller and less awkward aerodynamic cross section than a F9 fairing halve). See: https://m.youtube.com/watch?v=enndCzvZpZk
The problem with this and a fairing is that if the fairing catches the open side, it's going to drag behind like a giant parachute and take the plane down. The fairing is huge (13m long x 5m diameter), even compared to a big plane.