That's the proposal of one helicopter firm, and it wouldn't be the first time we've seen it.
Helicopters replacing tractors and cranes in order to remove stricken F1 cars? That is the proposal of Swiss helicopter firm Air Zermatt and although the idea seems a bit out there and over the top, it's been tested before.
In 2005, A1GP tried out a helicopter car recovery system, as seen in the following video. The burning question remains, would it actually be safer?
To me, there are multiple issues with such a method. For one, the risk for a different kind of disaster when someone is trying to use a helicopter to lift a mangled Formula One car could actually be more hazardous than the current way of doing it, not to mention the risk of debris falling from the car while it's hovering 30 feet in the air.
Unanticipated wind gusts, inclement weather, debris, cables snapping, other mechanical failures to name a few ... You're adding a plethora of new ways for the recovery of cars to go wrong.
Yes, you could avoid tragedies such as the one we saw in Suzuka, but you're also opening the door to a potentially worse situation taking place. This idea still puts men on the ground at risk in danger, same as they would be with a crane because somebody has to hook that car up.
There's a much simpler and easier solution
Overall, it's just a bad idea. You're eliminating certain risks, but only creating an entire lot of new ones in the process. It's like taking one step forward and two steps back. Here's a much easier and simpler solution ... When a car is stuck on the track, either deploy the Safety Car or employ a mandatory, snails-pace speed limits under local yellows.