@ The Natural Philosopher
Kinetic energy extractable from the air is a function of
the *relative* velocity between the machine extracting
the energy, and the air.

This is true for a device extracting energy through a turbine
mechanism, but not for a device extracting energy from the air using a
propeller.

First, let’s summarize the difference between a prop and a turbine:
In short and simplistic terms, a turbine slows air down relative to
itself, and uses that extracted energy to provide an *output torque*
on the rotor shaft. A propeller requires an *input torque* at its
shaft, and uses that input torque to accelerate air relative to
itself.

One way to highlight the differences in the two mechanisms is to
imagine being on a skateboard on a busy city sidewalk (where for our
purposes everyone is walking the same direction).

If I'm on the skateboard and I just cross my arms and stand still on
the board, I will gradually get pushed down the sidewalk as people
bump into me one by one. I will be extracting energy from each of the
people who contact me - slowing them down just a bit, and obviously I
can never quite reach the speed of those who bump into me. If (though
other means) I manage to attain the speed of the travelers on the
sidewalk, it’s obviously impossible to extract any energy from them at
all. This is the turbine analogy – like the people on the sidewalk,
the air molecules strike the passive blades just as the people strike
the passive skateboarder.

The propeller device works quite different and has a different set of
limitations.

Now imagine me on the same skateboard on the same busy sidewalk, but
instead of simply crossing my arms and passively waiting for
pedestrians to strike me and bump me down the walk to my destination I
quite literally take matters into my own hands – I reach out and push
people backwards while propelling myself forwards. In this scenario,
I can extract *more* energy from each person (I can push back on them
hard enough to bring them to a complete stop, unlike the turbine). I
can also continue to extract energy from people even when I am going
faster than they are as unlike the turbine, I am no longer just
waiting for them to hit me. As I rip down the sidewalk say twice as
fast as everyone else, there’s nothing stopping me from grabbing
everyone I come up on and pushing them backwards to a stop – and
taking all their KE in the process.

So, taking us back to the the assertion quoted at the top of the post
-- one can see that it's a true assertion when applied to a passive
turbine device which *does* rely on the relative motion between air
and machine to extract energy. It's not a true assertion however when
applied to a device which can actively push back on the molecules of
air -- such a device can continue to extract energy from the air even
when it's relative motion is exactly the same as the average speed of
the molecules.

The primary limitation on the propeller device? -- we have to find
the energy somewhere to provide the input torque to turn it. To put
it back in the skateboard example, the energy to power my arms has to
come from somewhere and in this case, it can come from the skateboard
wheels.

If anyone wishes see the math which shows there is ample power
available at the wheels of the skateboard to accomplish this task, I’m
quite happy to walk through it.