Why do gyros use tilt head rather than swashplate

The change in direction of the airflow between a nose down
attitude under power in a helo and a nose up, direction slightly
down for autorotation makes the mechanical aoa at the hub
different from the aoa of the airflow on the rotor.

Not sure what you mean by mechanical AoA at the hub, but the AoA of the
blades increases (more +ve), for the same pitch angle, with an upward
flowing airstream.

I think what they're refering to when they say "mechanical AoA" is blade
incidence.

Fixed wing aircraft generally have their wings set a some positive incidence
relative to the long axis (longitudinal) of the fuselage. The main reason for
this, as I understand it, is so the fuse will fly in a level attitude at cruise
while allowing the wing to fly at a positive AoA to produce the lift needed to
maintain flight. This positive incidence is fixed and cannot be changed or
adjusted by the pilot.

Helicopters, OTOH, adjust the incidence of their rotor blades through
collective and cyclic commands. In this case, the incidence is a measurement
of the angle of the rotor blade cord line relative to an imaginary line running
perpendicular (90 degrees to) the rotor mast. While changing the incidence of
the main rotor blades (through collective and cyclic commands) will change the
aerodynamic AoA, they are not the same thing. For example, if you could lower
the collective to a negative "incidence" (I'm not sure if full size helicopters
do this, I know that RC models do), the rotor blades would still be seeing a
positive AoA while in flight due to the steep descent angle.

FWIW,
Fly SAfe,
Steve R.