Arms generally do better on a slower court in terms of shock and torsion strains per stroke, because a slower ball transmits less shock and torsion through the racquet to the arm. Torsion is the twisting force caused by hitting off center on your strings; slow hard courts minimize off-center hits by providing a true bounce and more time to line up each shot.
On a slow hard court, it's more difficult to win points by simply blasting away, so players learn to be more patient and think beyond the current shot, for example by hitting a sharp angle to open up the court for the next shot. With longer points and better shot placements, players run more and get better exercise, and except for rubberized courts that get too sticky in the heat, slow hard courts make the safest running surface, as the traction is excellent.
The rough, but firm grain of a slow hard court surface bites deeply into the ball's fuzz, so that any spin on the ball has a pronounced effect on its bounce. Sidespins curve more sideways, soft backspins bounce more backward (or less forward), and topspins bounce higher than they would on a faster surface. Sidespins especially are more effective on a slow hard court than on the other slow surface, clay, where much of the sideward force of the spin is wasted scattering clay particles outward as the ball bounces.