After all, the centrifugal and coriolis effects are only very special cases
of the general rule essential to the Newtonian model: Don't expect this
physics to work if you are not in an inertial frame - the effects of YOUR
acceleration will make muddy the waters.
An observer in a general state of acceleration will be hard pressed to find
the proper fudge factors to make sense of his observations. We have done
the "un-muddying" for the rotating observer only because it is do-able
(that's all we ever study in texts/classes) and because we happen to be in
just that state of acceleration (ignoring some other, smaller effects).
There is otherwise no fundamental reason for singling out the
centrifugal/coriolis effects from among the infinite possibilities of
"observer-accelerated " effects.