De-spinning

A flywheel is only a temporary store for momentum/energy,
it is not a source nor a sink.

A flywheel has a maximum allowable spin before it disintegrates due to
tensile stresses.

Hence, all fyhweels need to be desaturated, or the momentum must be
dumped somewhere.
In space, the only way to dump momentum is to find some a method of
applying force,
i.e. some external thrust. In conventional spacecraft today moemtum
wheels are
desaturated by firing thrusters to take out the energy while electrical
"brakes" are
applied to the wheels.

In most cases, since you have to carry propellant anyway to desaturate
the wheels, the
wheels actually do not buy you very much. In practice, the primary
purpose for momentum
wheels on spacecraft is to provide an extremely stable platform for
accurately pointing either
cameras or radio antennae.

To despin an asteroid, a wheel would have little value, we might as well
use thrusters and cut out
the middle man. For such a wheel to be effective for depsinning an
asteroid it would have to be
very large, and would weigh more than the rest of the spacecraft put
together.

=====

Nobody has addressed the amount of propellant which would eb needed for
retrieving an asteroid.
It is very large.

Nobody has mentioned the studies done by Dr. Brian O'Leary in the 1970's
for retrieving asteroids using mass drivers. The mass of the asteroid
itself is used as reaction mass for the mass driver.
IIRC about half of the mass of a typical NEO would need to be ground up
and used as reaction mass to get the remained back to Earth. This
would save a lot by eliminating the need to ship
propellant all the way from Earth.

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