The main reason for starting "slow" is that
not all combs in the extractor are created equal.
The initial spins are to remove the "extra" honey
so that one has a somewhat "balanced" load of
frames before going up to higher speeds.
Assuming that you are using a tangential
extractor, a higher extractor speed
(higher tangential velocity) is going
to create a spike in centripetal acceleration
for the combs that contain the most honey.
You remember good old Newton, and his
"Force = Mass * Acceleration" equation,
so the problem faced when extracting honey
is that we want to avoid applying too much
acceleration until all the combs contain
roughly equal mass.
Even with a hand-cranked extractor, you can
see (and FEEL) this. The extractor acts like
a bucking horse for a while.
This is why one can find "automated" speed
controls, which slowly increase the rotational
speed as time passes. (I've never seen one
that only speeds up the motor when it detects
a non-vibrating shaft, which would be better.)