The title is complete clickbait. It should say “no one’s short intuitive explanations of why planes stay in the air are fully correct”
Just as no one can explain how bicycles stay up once they get moving. Or why hot air rises but it's always cold in the mountains when they should be hot from all that rising hot air.
We know why paper airplanes stay in the air. They are lifted up by hot air from the teachers they are thrown at.
I'd say reaction force is a sufficient explanation. The wing compresses the air column below it. The pressurised air generates buoyancy sufficient to dynamically support the air craft while moving at a high enough speed.
There's a very famous book called Stick and Rudder that does a good job of explaining this. A plane stays up because of Newtonian reaction. The Bernloulli principle and its associated airfoil shape should be thought of as an efficient way of displacing air downwards without the appearance of the wing being angled upwards.
IOW a classic airfoil that appears horizontal is really best thought of as a flat surface that's angled upwards. When a plane with a wing like that inverts, it really does "lift" downwards, and it takes considerable elevator correction to keep level.
If the wing had a symmetric airfoil section, then it needs to be visibly angled upwards in order to fly; but on the other hand when upside down it doesn't take as much elevator input to stay up as the classic asymmetric version.