FE Banjo guy, while I like him, isn't always particularly careful, and sometimes makes some bad argument. So, the response from the rotating-globe-earth crowd to the rotation of the earth under a plane is that gravity and the closed atmospheric system drag the plane alone with it.
But there's a huge problem with this that the Globers don't address. If that's the case, then a plane travelling from East to West would have to overcome these tremendous forces. Remember that this force drags the plane around at 1,000MPH (at the equator), and that's a tremendous amount of force. So, then flying against, these forces, from East to West, that would be like a fish swimming upstream, and planes would need a tremendous amount of additional fuel going in that direction vs. the other. And flights going West would take longer than flights going East. But there's no difference whatsoever in time or fuel consumption.
Here's an example to illustrate the problem. You know those moving walkways they have (typically at airports), where there's a belt that moves people so that they don't have to walk with their luggage. Kids especially tend to goof around on those and then walk in the opposite direction. Or you also see people trying to go up downward-moving escalators. It requires a tremendous amount of extra energy to go AGAINST the direction that these things are moving, since you have to overcome the forces that are taking you in the other direction.
So the Globers constantly contradict themselves, talking about forces that are present when it's convenient but then disappear when they're not convenient.
We had the RedBull guy take about 2.5-3 hours to ascend to about 120,000 feet, from which he jumped. During that time the earth would have rotated about 1500 miles (if I recall, given his latitude). But after he jumped, instead of ending up about 1500 miles to the West, in the Pacific Ocean, he landed about 20-30 miles East of where he took off from. So even at those altitudes, the capsule was held steady by the iron rod of gravity (and then perhaps the wind pushed him East). Also, as you get higher, to keep up with the ground below, your movement around the earth actually has to accelerate, since the circuмference of your rotation has to increase. Of course, that's another thing. Wind patterns move from West to East, and that means that the atmosphere is moving faster than the earth's rotation, in excess of 1000MPH at the equator, several times faster than the highest wind speeds ever recorded in a tornado.
North to south flights are even a bigger problem. As you go from North to South, your angular momentum constantly increases, as the speed of the earth beneath increases. Finally, an engineer was won over by the argument that he laid out that if a plane is travelling, say, West to East, and then had to turn on its final approach to hit a North-South runway, that turn from going with the rotation for the earth to suddenly going North-South would put such force on the plane that it would get torn apart, not to mention that landing on a North-South runway would be nearly impossible to pull off.
These forces that would drag objects from West to East simply don't exist.