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?

Thanks in advance for enlightening me,
Oliver