writes:

In a situation like that, what would be most important would be her ability
to stay calm, not panic and fly the airplane.

She'll need to be able to follow instructions to fly the airplane. Most people
won't panic in a situation like that, although they may be very anxious.

Look around at the average non-pilots in an airliner when a sudden noise
like the gear coming up happens and you will see lots of faces with
momentary fear and it gets worse with even the mildest of turbulence.

When I look around at passengers in an airliner cabin, I usually don't see
anyone who even notices the noise of the gear retracting, and most ignore
turbulence as well unless it spills their drinks.

The reality is the average non-pilot is afraid of flying to some extent or
other and becomes frightened at just about every bump or sudden change in
the background noise.

Only a minority of people have a fear of flying, although it's a substantial
minority (around 14% according to some estimates, if I remember correctly).
The rest are non-pilots without fear.

My opinion is all the sensory inputs (of which those only "flying" sims
have no clue) ...

The sensory inputs are the same for pilots as they are for passengers.

... along with the the huge responsibility of flying an aircraft
full of other people would likely overwhelm the average non-pilot.

You greatly exaggerate the special character of flying. It doesn't scare
people that much (or at all), and they do not instantly panic when things go
wrong.

And since all pilots are trained "to follow instructions precisely", that
becomes two reasons that a random pilot has better chances of success than
a random non-pilot.

Pilots are trained to take responsibility and fly the airplane themselves.
Taking instructions is secondary to that.