Why does airspeed change when I adjust the prop?

Anno v. Heimburg writes:

And the gearbox-metaphor is not very well suited because most cars don't
have a contiously-variable transmission ...

FWIW, I did have a scooter with this type of transmission. It was a
bit bizarre, because if you opened the throttle wide open from a
standing start, the engine would speed up to its optimal RPM, and then
the transmission would continuously change ratios to keep the engine
at the same RPM as the scooter accelerated. You'd hear a constant
whirr from the engine, even though you were accelerating very rapidly.
It also provided good acceleration because of this, since the
(relatively small) engine was held at a single optimum speed.

That is not the case with the constant-speed prop, you select a desired
rpm, and the prop governor adjusts the load on the engine (by varying the
prop pitch) to maintain that rpm, regardless of the actual power output of
the engine (within the limits of the prop's abilities, of course).

So what do you gain with the prop adjustment? Just a reduction in
wear and tear and/or noise?

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