Ignoring any questions about salts of whatever kind- soft-water ice tastes nasty, especially if it sits in the freezer awhile in a self-defrost unit. The actual h20 evaporates off, and the trace element load increases. I almost never use ice because it tastes so bad, and the cubes are usually half-evaporated. It leaves a nasty residue in bin and chute, and the chilled water tube is almost plugged. On the other hand, I the in-door water and ice at my sister's place, with no softener. If I ever get around to getting a plumber in here to clean up the punch list of piddly projects, one of them will be replacing ice maker saddle tap in basement with a coupling, and running a new feed off a tee attached to an accessible unsoftened cold line near the feed from the well, with a shutoff valve to make the inline filter painless to change.
One of these days....
-- aem sends...