I can imagine that some limescale might still build up in the pipe or faucet even with softened water. If extremely low-lime water then sits in the pipe, it might dissolve limescale from the deposits again. As a non-chemist, I can't say whether this has anything to do with the high sodium content.
Our Berlin "concrete water" tastes quite good, even though it grits between the teeth. But I always let some water run because I like it cold.
, maybe I should still consider a circulation line for cold water ;-)