ORIGINAL: Shoe

What if instead, you increased the distance between the rotor disk and the ground plate (with fixed plate size)? I think most would also agree that beyond a certain critical rotor-to-plate separation, the helicopter would also be able to lift off.
I agree.
For any given rotor-plate separation, can you always make the plate big enough to keep the helicopter on the ground (assuming the plate doesn't get heavier as it gets bigger)? I think most would say "yes you can".
I disagree. It seems to contradict your first statement. What if the given separation were 60 meters?
Suppose that there were a scale under the foam plate in the video. Would the scale reading go down as you applied collective? If so, how would the size of the plate effect this? Could you make the plate big enough so that the scale reading wouldn't change at all as you applied collective?
I think (given the separation distance in the video) the scale reading would go down as the plates radius is reduced to less than that of the rotors radius. The scale would directly measure mg-ma.
What does this have to do with Bernoulli and Newton? Well, suppose that you COULD make the plate big enough so that the scale reading wouldn't change with collective. And suppose further that no matter how much you separated the rotor from the ground plate, you could always make the the plate big enough to keep the scale from changing with collective. This raises an interesting question about momentum. If the scale reading doesn't change, that suggest that the air exerts no NET vertical force on the helicopter-ground plate system. By Newton's third law, if the air exerts no net force on the helicopter-ground-plate system, then the helicopter-ground-plate system exerts no net force on the air. Newton's second law then leads us to the inescapable conclusion that the helicopter ground plate system can't be changing the NET vertical momentum in the air.

This should be troubling if you think that a helicopter flies by transferring momentum to the air. If the above is true, then if you consider a big enough piece of the earth's surface, the net downward force exerted by the helicopter on that surface is equal to the upward force on the helicopter (at any altitude). If that's the case, then the helicopter can't possibly be changing the momentum in the air. Yikes, that would certainly challenge my notions of how a helicopter flies!
I think that you could separate the rotor from a weightless plate enough that no matter how big the plate got the helicopter could still lift off and climb in altitude. Interplanetary space probes (Cassini, Magellan) make small course corrections using Newtons 3rd law and there is no air or planet to push against.