Why are low-revving, high torque engines preferred?

Oliver Arend schreef:
This may sound like a stupid question; I realize the prop can only
turn at a certain speed to avoid transonic effects at the tips and has
to be turned with a certain torque to transmit the power needed/
produce enough thrust. So far so good.

But why does the torque have to be produced by the engine in direct
drive? Couldn't weight and space be saved by using a high-revving,
small displacement engine (such as a car or even motorcycle engine)
with a reduction gearbox? I'm aware that a reduction gearbox will add
weight (but not that much?), complexity and failure modes, and that
transmitting the forces created by the prop to the airframe could be
an issue. Does it boil down to the price? Is a Lycosaur engine cheaper
than, say, a motorcycle engine of equivalent power plus the gearbox?

At the risk of feeding the trolls:
There are several examples of the setup you describe.
The Rotax 4-stroke engines have a (belt?) reduction.
In Europe one sees more and more BMW-motorcycle engines
driving planes through a reduction, either gear or belt.

I even seem to remember car/bike engines driving a prop through
the original gearbox, fixed in one gear; but never with good results.

The main disadvantage of automotive engines is that they were
never designed for delivering their output power over
a prolonged period of time, like an aircraft engine does.
This also applies to an even greater degree to motorbike engines.

But even in the country of Lycosaurs some people
are flying behind (or before...) car engine conversions,
you might wish to search for the Corvair engine in particular.

PS if you are interested in cheap engines for modest homebuilt planes,
read every page of Bob Hoover's blog, frequently mentioned on these pages.
Good reading both for wisdom and for technical insight!

Hope this helps,