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Ludwik,
It might help to realize that the effective potential U(r) is more
than just a helpful visualization tool for the inertial observer
(helping him to abstract from the angular motion and consider only the
one-dimensional radial motion, It is also the actual view which a
rotating observer would take of the planet. The added term in U(r) is
precisely the potential energy which a rotating observer would ascribe
to the centifugal force which he sees affecting the radial motion of
the planet. The radial motion is all that he sees, since he rotates
along with the angular motion of the planet. The rotating observer
indeed sees one dimensional motion in a potential energy well - no
paradox here.
I would say that there is no paradox for the inertial observer either,
because he realizes that this is not one-dimensional motion. Looking
only at V(r) ignores the important complicating effects of the angular
motion.